Probability

187 Practice MCQs available for CA Foundation

Paper

Paper 3: Quantitative Aptitude

Exam Weightage

5-7 Marks

Key Topics

Probability Operations, Expected Value

A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.

Exam Strategy Tip

Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.

Key Terms

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

Independent Events

Two events A and B are independent if the occurrence of one does not affect the probability of occurrence of the other. For independent events: P(A∩B) = P(A) × P(B).

All 187 Questions

3388
If P(A)=12\displaystyle P(A) = \frac{1}{2}, P(B)=13\displaystyle P(B) = \frac{1}{3}, P(A∩B)=14\displaystyle P(A \cap B) = \frac{1}{4}, then the value of P(A′∪B′)\displaystyle P(A' \cup B') is
MCQ
4079
Two dice are thrown simultaneously. Find the probability that the sum of digits on the two dice would be 8 or more.
MCQ
4080
A number is selected from the first 20 natural numbers. Find the probability that it would be divisible by 3 or 7.
MCQ
4081
A father had three sons namely, Kailash, Harish and Prakash. All are above 65 years in age. Prakash happens to be the eldest while Kailash as youngest. As per the health history, it is estimated that the probability that Kailash survives another 5 years is 45\displaystyle \frac{4}{5}, Harish survives another 5 years is 35\displaystyle \frac{3}{5} and Prakash survives another 5 years is 12\displaystyle \frac{1}{2}. The probabilities that Kailash and Harish survive another 5 years is 0.46, Harish and Prakash survive another 5 years is 0.32 and Kailash and Prakash survive another 5 years is 0.48. The probability that all three sons survive another 5 years is 0.26. What shall be the probability that at least one of them survives another 5 years?
MCQ
4082
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected is
MCQ
4083
Two cards are drawn from a pack of 52 cards. The probability that one is a spade and one is a heart; is
MCQ
4084
A problem is given to 5 students P, Q, R, S and T. If the probability of solving the problem individually is 12\displaystyle \frac{1}{2}, 13\displaystyle \frac{1}{3}, 23\displaystyle \frac{2}{3}, 15\displaystyle \frac{1}{5} and 16\displaystyle \frac{1}{6} respectively, then find the probability that the problem is solved.
MCQ
4085
In a leap year, what is the probability that there will be 53 Sundays?
MCQ
4179
The number of tosses of a coin, that are needed so that the probability of getting at least one head is 0.875, is
MCQ
4180
Two-person X and Y appear in an interview for two vacancies for the same post. The probability of X's selection is 1/5 and that of Y's selection is 1/3. The probability that none of them will be selected is
MCQ
4181
A number is selected at random from the first 50 natural numbers. What is the probability that it would be either a two-digit prime number or a composite number lying between 5 and 40?
MCQ
4182
Some dice with six faces have numbers written from Four to Nine. Two such dice are thrown simultaneously. Find the probability that the sum of numbers on the two dice would be 14 or less.
MCQ
4183
Three components A, B and C are manufactured separately and then assembled into a finished product. While producing the three components, it is found that 5 percent of component A, 4 percent of component B and 1 percent of component C are defective. What is the probability that the assembled product is free from defects?
MCQ
4184
Two persons are playing a set of matches. The winner of 4 matches is declared as the winner. Any player has 50% chance to win a match. The probability that the game comes to an end at the fourth match is
MCQ
4238
Find the probability that a 3-digit number formed using the digits 1, 3, and 5 (without repetition), is divisible by 3?
MCQ
4239
Ms. Radhika appeared in interview at three different companies. In the first company there are 5 candidates, in second company there are 12 candidates and in third company there are 15 candidates. What is probability that Ms. Radhika would be selected?
MCQ
4240
The odds in favour of Mr. A to solve a problem is 5:7 and odds against to Mr. B to solve the same problem is 9:6. What is the probability that if both of them try, the problem will be solved?
MCQ
4289
If in a class, 50% of the student study mathematics and science and 70% of the student study mathematics, then the probability of a student studying science given that he/she is already studying mathematics is
MCQ
4290
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
MCQ
4291
If two dice are rolled, then the probability of getting a greater number on the first die than the one on the second, given that the sum should be equal to 7 is
MCQ
3335
The probability that a four digit number comprising the digits 2,5,6\displaystyle 2, 5, 6 and 7\displaystyle 7 without repetition of digits, would be divisible by 4\displaystyle 4 is
MCQ
3394
If P(A)=12\displaystyle P(A) = \frac{1}{2}, P(B)=13\displaystyle P(B) = \frac{1}{3} and P(A∩B)=14\displaystyle P(A \cap B) = \frac{1}{4}, what is P(A/B)\displaystyle P(A/B)?
MCQ
3324
If A\displaystyle A speaks 75%\displaystyle 75\% of truth and B\displaystyle B speaks 60%\displaystyle 60\% of truth. In what percentage both of them likely contradict with each other in narrating the same questions?
MCQ
3357
Thirty balls are serially numbered and placed in bag. Find chance that the first ball drawn is a multiple of 3\displaystyle 3 or 5\displaystyle 5
MCQ
3408
From the following probability distribution table, find E(x)\displaystyle E(x):X | 1 | 2 | 3f(X) | 12\displaystyle \frac{1}{2} | 13\displaystyle \frac{1}{3} | 16\displaystyle \frac{1}{6}
MCQ
3407
If 2x+3y−4=0\displaystyle 2x + 3y - 4 = 0 and V(x)=6\displaystyle V(x) = 6 then V(y)\displaystyle V(y) is
MCQ
3279
Two dice are thrown simultaneously. The probability of a total score of 5\displaystyle 5 from the out comes of dice is.
MCQ
3347
Two events A&B Probabilities 0.24\displaystyle 0.24 and 0.52\displaystyle 0.52 respectively. If the probability of both A and B occurs simultaneously is 0.15\displaystyle 0.15. Then the probability that neither A nor B occur is 0.15\displaystyle 0.15, then the probabilities that neither A nor B is.
MCQ
3400
The probability distribution of the demand for a commodity is given belowX | 5 | 6 | 7 | 8 | 9 | 10P(X) | 0.05 | 0.10 | 0.30 | 0.40 | 0.10 | 0.05Expected value of demand will be
MCQ
3315
If P(A∪B)=0.8\displaystyle P(A \cup B) = 0.8 and P(A∩B)=0.3\displaystyle P(A \cap B) = 0.3, then P(A)+P(B)\displaystyle P(A) + P(B) is equal to
MCQ
3295
If P:Q\displaystyle P: Q is the odds in favor of an event, then the probability of that event is
MCQ
3345
The probability of success of three students in CA Foundation examination are 1/5,1/4\displaystyle 1/5, 1/4 and 1/3\displaystyle 1/3 respectively. Find the probability that at least two students will get success.
MCQ
3402
If a random variable X\displaystyle X assumes the values x1,x2,x3,x4\displaystyle x_1, x_2, x_3, x_4 with corresponding probabilities, P1,P2,P3,P4\displaystyle P_1, P_2, P_3, P_4 then the expected value of X\displaystyle X is
MCQ
3341
A question in statistics is given to three students A, B and C. Their chances of solving the question are 1/3,1/5\displaystyle 1/3, 1/5 and 1/7\displaystyle 1/7 respectively. The probability that the question would be solved is
MCQ
4379
Two dice are thrown simultaneously. Find the probability that the sum of digits on the two dice would be 8 or more.
MCQ
4380
A number is selected from the first 20 natural numbers. Find the probability that it would be divisible by 3 or 7.
MCQ
4381
A father had three sons namely, Kailash, Harish and Prakash. All are above 65 years in age. Prakash happens to be the eldest while Kailash as youngest. As per the health history, it is estimated that the probability that Kailash survives another 5 years is 45\displaystyle \frac{4}{5}, Harish survives another 5 years is 35\displaystyle \frac{3}{5} and Prakash survives another 5 years is 12\displaystyle \frac{1}{2}. The probabilities that Kailash and Harish survive another 5 years is 0.46, Harish and Prakash survive another 5 years is 0.32 and Kailash and Prakash survive another 5 years is 0.48. The probability that all three sons survive another 5 years is 0.26. What shall be the probability that at least one of them survives another 5 years?
MCQ
4382
In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected is
MCQ
4383
Two cards are drawn from a pack of 52 cards. The probability that one is a spade and one is a heart; is
MCQ
4384
A problem is given to 5 students P, Q, R, S and T. If the probability of solving the problem individually is 12\displaystyle \frac{1}{2}, 13\displaystyle \frac{1}{3}, 23\displaystyle \frac{2}{3}, 15\displaystyle \frac{1}{5} and 16\displaystyle \frac{1}{6} respectively, then find the probability that the problem is solved.
MCQ
4385
In a leap year, what is the probability that there will be 53 Sundays?
MCQ
4479
The number of tosses of a coin, that are needed so that the probability of getting at least one head is 0.875, is
MCQ
4480
Two-person X and Y appear in an interview for two vacancies for the same post. The probability of X's selection is 1/5 and that of Y's selection is 1/3. The probability that none of them will be selected is
MCQ
4481
A number is selected at random from the first 50 natural numbers. What is the probability that it would be either a two-digit prime number or a composite number lying between 5 and 40?
MCQ
4482
Some dice with six faces have numbers written from Four to Nine. Two such dice are thrown simultaneously. Find the probability that the sum of numbers on the two dice would be 14 or less.
MCQ
4483
Three components A, B and C are manufactured separately and then assembled into a finished product. While producing the three components, it is found that 5 percent of component A, 4 percent of component B and 1 percent of component C are defective. What is the probability that the assembled product is free from defects?
MCQ
4484
Two persons are playing a set of matches. The winner of 4 matches is declared as the winner. Any player has 50% chance to win a match. The probability that the game comes to an end at the fourth match is
MCQ
4538
Find the probability that a 3-digit number formed using the digits 1, 3, and 5 (without repetition), is divisible by 3?
MCQ
4539
Ms. Radhika appeared in interview at three different companies. In the first company there are 5 candidates, in second company there are 12 candidates and in third company there are 15 candidates. What is probability that Ms. Radhika would be selected?
MCQ
4540
The odds in favour of Mr. A to solve a problem is 5:7 and odds against to Mr. B to solve the same problem is 9:6. What is the probability that if both of them try, the problem will be solved?
MCQ
4589
If in a class, 50% of the student study mathematics and science and 70% of the student study mathematics, then the probability of a student studying science given that he/she is already studying mathematics is
MCQ
4590
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
MCQ
4591
If two dice are rolled, then the probability of getting a greater number on the first die than the one on the second, given that the sum should be equal to 7 is
MCQ
3322
What is the probability of getting 7\displaystyle 7 or 11\displaystyle 11 when two dice are thrown?
MCQ
3264
According to bayee's theorem, P(Ei/A)=P(Ei)P(A/Ei)∑j=1nP(Ej)P(A/Ej)\displaystyle P(E_i / A) = \frac{P(E_i)P(A / E_i)}{\sum_{j=1}^{n} P(E_j)P(A / E_j)} here
MCQ
3265
When 2\displaystyle 2 - dice are thrown simultaneously then the probability of getting at least one 5\displaystyle 5 is
MCQ
3266
A log contains 15\displaystyle 15 one rupee coins, 25\displaystyle 25 two rupees coins and 10\displaystyle 10 five rupee coins if a coin is selected at random than probability for not selecting a one rupee coin is:
MCQ
3267
What is the probability of occurring 4\displaystyle 4 or more than 4\displaystyle 4 accidents.No. of acc. | Frequency0 | 361 | 272 | 233 | 244 | 245 | 276 | 187 | 9
MCQ
3268
When two coins are tossed simultaneously the probability of getting at least one tail?
MCQ
3269
Two broad divisions of probability are
MCQ
3270
The term "chance" and probability are synonyms:
MCQ
3271
Sum of all probabilities mutually exclusive and exhaustive events is equal to
MCQ
3272
The probability that a leap year has 53\displaystyle 53 Wednesday is
MCQ
3273
Two different dice are thrown simultaneously, then the probability that the sum of two numbers appearing on the top of dice is 9\displaystyle 9 is:
MCQ
3274
Two event A\displaystyle A and B\displaystyle B are such that they do not occurs simultaneously then they are called events
MCQ
3275
When 3\displaystyle 3 dice are rolled simultaneously the probability of a number on the 3rd\displaystyle 3^{rd} dice is greater than the sum of the numbers on two dice.
MCQ
3276
An event that can be subdivided into further events is called as.
MCQ
3277
Three identical and balanced dice are rolled. The probability that the same number will appear on each of them is.
MCQ
3278
A basket contains 15\displaystyle 15 white balls, 25\displaystyle 25 red balls and 10\displaystyle 10 blue balls. If a ball is selected at random, the probability of selecting not a white ball.
MCQ
3280
If an unbiased coin is tossed onece, then the probability of obtaining at least one tail is.
MCQ
3281
If an unbiased coin is tossed three times, what is the probability of getting more than one head?
MCQ
3282
Which of the following pair of events E\displaystyle E and F\displaystyle F are mutually exclusive?
MCQ
3283
What is the probability of occurrence of leap year having 53\displaystyle 53 Sunday?
MCQ
3284
Two perfect dice are rolled what is the probability that one appears at least in one of the dice?
MCQ
3285
If p,q\displaystyle p, q are the odds in favour of an event, then the probability of that event is -
MCQ
3286
The probability that a leap year has 53\displaystyle 53 Monday is:
MCQ
3287
If a number is selected at random from the first 50\displaystyle 50 natural numbers, what will be the probability that the selected number is a multiple of 3\displaystyle 3 and 4\displaystyle 4?
MCQ
3288
If three coins are tossed simultaneously, what is the probability of getting two heads together?
MCQ
3289
Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The probability that exactly 2 of them are children is
MCQ
3290
A box contain 20 electrical bulbs out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of them is defective.
MCQ
3291
If a card is drawn at random from a pack of 52 cards, what is the chance of getting a Club or a King?
MCQ
3292
Eight labourers are working at a construction side with the following wages for each day of working (in ₹): 500, 620, 400, 700, 450, 560, 620, 450. If one of the workers is selected at random, what is the probability that his wage would be less than the average wage?
MCQ
3293
A box contains shoe pairs of same pattern of different sizes numbered from 1 to 12. If a shoe pair is selected at random, what is the probability that the number on the shoe pair will be a multiple of 3 or 6?
MCQ
3294
Two cards are drawn at random from a pack of 52 cards. The probability of getting either both the red cards or both Kings cards is:
MCQ
3296
If P(A)=49\displaystyle P(A) = \frac{4}{9}, then odd against the event 'A' is
MCQ
3297
The probability of A solving a problem is 712\displaystyle \frac{7}{12} odds against solving a problem
MCQ
3298
When 2\displaystyle 2 dice are thrown simultaneously then the probability of getting at least one 5\displaystyle 5 is:
MCQ
3299
The probability that a leap year has 53\displaystyle 53 Wednesday is:
MCQ
3300
Ticket number 1\displaystyle 1 to 20\displaystyle 20 are mixed and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is multiple of 3\displaystyle 3 or 7\displaystyle 7?
MCQ
3301
The probability that a leap year has 53\displaystyle 53 Sunday is:
MCQ
3302
If a card is drawn randomly from a deck, the probability of the card being neither a red card nor a face card?
MCQ
3303
If two dice are thrown then what is the probability that the sum of the faces of dice are square or cube number?
MCQ
3304
If a card is drawn at random from a pack of cards, what is the chance of getting spade or an ace?
MCQ
3305
The chance of getting a sum of 10\displaystyle 10 in a simple single throw is
MCQ
3306
Exactly 3\displaystyle 3 girls are to be selected from 5\displaystyle 5 girls and 3\displaystyle 3 boys. The probability of selecting 3\displaystyle 3 girls will be
MCQ
3307
A bag contains 15\displaystyle 15 one rupee coins, 25\displaystyle 25 two rupee coins and 10\displaystyle 10 five rupee coins. If a coin is selected at random from the bag, then the probability of not selecting a one rupee coin is:
MCQ
3308
A letter is taken out at random from the word RANGE and another is taken out from the word PAGE. The probability that they are the same letters is
MCQ
3309
If P(A)=4:9\displaystyle P(A) = 4:9, then odd against the event 'A' is
MCQ
3310
If p:q\displaystyle p:q is the odds in favor of an event, then the probability of that event is -
MCQ
3311
There are two boxes containing 5\displaystyle 5 white and 6\displaystyle 6 blue balls and 3\displaystyle 3 white and 4\displaystyle 4 blue balls respectively. If one of the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is
MCQ
3312
A box contains 5\displaystyle 5 white and 7\displaystyle 7 black balls. Two successive drawn of 3\displaystyle 3 balls are made (i) with replacement (ii) without replacement. The probability that the first draw would produce white balls and the second draw would produce black balls are respectively.
MCQ
3323
When 2\displaystyle 2 fair dice are thrown, what is the probability of getting the sum which is a multiple of 3\displaystyle 3?
MCQ
3313
X\displaystyle X and Y\displaystyle Y are stand in a line with 6\displaystyle 6 people. What is the probability that there are three persons between them?
MCQ
3314
Ram is known to hit a target in 2\displaystyle 2 out of 3\displaystyle 3 shots where as Shyam is known to hit the same target in 5\displaystyle 5 out of 11\displaystyle 11 shots. What is the probability that the target would be hit if they both try?
MCQ
3316
If a coin is tossed 5\displaystyle 5 times then the probability of getting Tail and Head occurs alternatively is
MCQ
3317
Two letters are chosen from the word HOME. What is the probability that the letters chosen are not vowels.
MCQ
3318
If A,B,C\displaystyle A, B, C are three mutually exclusive and exhaustive events such that: P(A)=2P(B)=3P(C)\displaystyle P(A) = 2P(B) = 3P(C) what is P(B)\displaystyle P(B)?
MCQ
3319
What is the probability of having at least one '6\displaystyle 6' in 3\displaystyle 3 throws of a project die?
MCQ
3320
If P(A)=12\displaystyle P(A) = \frac{1}{2}, P(B)=13\displaystyle P(B) = \frac{1}{3} and P(A∩B)=14\displaystyle P(A \cap B) = \frac{1}{4} then P(A∪B)\displaystyle P(A \cup B) is equal to
MCQ
3321
A coin is tossed six times, then the probability of obtaining heads and tails alternatively is
MCQ
3325
If there are 48\displaystyle 48 marbles market with numbers 1\displaystyle 1 to 48\displaystyle 48, then the probability of selecting a marble having the number divisible by 4\displaystyle 4 is;
MCQ
3326
A bag contains 7\displaystyle 7 blue and 5\displaystyle 5 green balls. One ball is drawn at random. The probability of getting a blue ball is_______.
MCQ
3327
The probability that a football team loosing a match at Kolkata is 3/5\displaystyle 3/5 and winning a match at Bengaluru is 6/7\displaystyle 6/7; the probability of the team winning at least one match is
MCQ
3328
A biased coin is such that the probability of getting a head is thrice the probability of getting a tail, if the coin is tossed 4\displaystyle 4 times, what is the probability of getting a head all the times?
MCQ
3329
If there are 16\displaystyle 16 phones, 10\displaystyle 10 of them are Android and 6\displaystyle 6 of them Apple, then the probability of 4\displaystyle 4 randomly selected phones to include 2\displaystyle 2 Android and 2\displaystyle 2 Apple phone is:
MCQ
3330
A dice is rolled twice. Find the probability of getting numbers multiple of 3\displaystyle 3 or 5\displaystyle 5?
MCQ
3331
If in a bag of 30\displaystyle 30 balls numbered from 1\displaystyle 1 to 30\displaystyle 30. Two balls are drawn find probability of getting a ball being multiple of 2\displaystyle 2 or 3\displaystyle 3
MCQ
3332
If P(A)=0.3\displaystyle P(A) = 0.3; P(B)=0.8\displaystyle P(B) = 0.8 and P(BA)=0.5\displaystyle P\left(\frac{B}{A}\right) = 0.5, find P(A∪B)\displaystyle P(A \cup B)
MCQ
3333
If P(A)=13\displaystyle P(A) = \frac{1}{3}, P(B)=34\displaystyle P(B) = \frac{3}{4} and P(A∩B)=1112\displaystyle P(A \cap B) = \frac{11}{12} then P(BA)\displaystyle P\left(\frac{B}{A}\right) is:
MCQ
3334
For any two events 'A' and 'B' it is known that P(A)=2/3\displaystyle P(A) = 2/3, P(B)=3/8\displaystyle P(B) = 3/8 and P(A∩B)=1/4\displaystyle P(A \cap B) = 1/4, then the events A and B are:
MCQ
3336
If P(A)=1/2\displaystyle P(A) = 1/2 and P(B)=1/3\displaystyle P(B) = 1/3 and P(A∩B)=2/3\displaystyle P(A \cap B) = 2/3 then find P(A∩B)\displaystyle P(A \cap B)
MCQ
3337
A number is selected from the first 30\displaystyle 30 natural numbers. What is the probability that it would be divisible by 3\displaystyle 3 or 8\displaystyle 8?
MCQ
3338
If P(A∩B)=13\displaystyle P(A \cap B) = \frac{1}{3}, P(A∪B)=56\displaystyle P(A \cup B) = \frac{5}{6} P(B)=23\displaystyle P(B) = \frac{2}{3} then P(Aˉ)\displaystyle P(\bar{A}) is:
MCQ
3346
If P(A)=0.65\displaystyle P(A) = 0.65 and P(B)=0.15\displaystyle P(B) = 0.15, then P(A)+P(B)\displaystyle P(A) + P(B) is:
MCQ
3339
A number is selected at random from the first 100\displaystyle 100 natural numbers. What is the probability that it would be a multiple of 3\displaystyle 3 or 7\displaystyle 7?
MCQ
3340
A number is selected at random from the set {1,2,…,99}\displaystyle \{1, 2, \dots, 99\}. The probability that it is divisible by 9\displaystyle 9 or 11\displaystyle 11 is
MCQ
3342
A company produces two types of products, A and B. The probability of defective product in type A is 0.05\displaystyle 0.05 and in type B is 0.03\displaystyle 0.03. If the company produces 60%\displaystyle 60\% type A and 40%\displaystyle 40\% type B, what is the probability of a randomly selected product being defective?
MCQ
3343
Which one holds correct for any two events A and B?
MCQ
3344
Which of the following pairs of events are mutually exclusive?
MCQ
3348
If P(A∩B)=0\displaystyle P(A \cap B)=0, then the two events A\displaystyle A and B\displaystyle B are
MCQ
3349
If A,B\displaystyle A, B and C\displaystyle C are mutually exclusive and exhaustive events, then P(A)+P(B)+P(C)\displaystyle P(A) + P(B) + P(C) equals to
MCQ
3350
Addition Theorem of Probability states that for any two events A\displaystyle A and B\displaystyle B
MCQ
3351
Three events A,B\displaystyle A, B and C\displaystyle C are mutually exclusive, exhaustive and equally likely. What is the probability of the complementary event of A\displaystyle A?
MCQ
3352
Find the probability that a four-digit number comprising the digits 2,5,6\displaystyle 2, 5, 6 and 7\displaystyle 7 would be divisible by 4\displaystyle 4.
MCQ
3353
If A\displaystyle A and B\displaystyle B are two events such that P(A)=1/4\displaystyle P(A) = 1/4, P(B)=1/3\displaystyle P(B) = 1/3 and P(A∪B)=1/2\displaystyle P(A \cup B) = 1/2, then P(B/A)\displaystyle P(B/A) is equal to
MCQ
3354
If A\displaystyle A and B\displaystyle B are two events and P(A)=2/3\displaystyle P(A) = 2/3, P(B)=3/5\displaystyle P(B) = 3/5, P(A∪B)=5/6\displaystyle P(A \cup B) = 5/6, then the value of P(A′/B′)\displaystyle P(A'/B') is :
MCQ
3355
P(A)=0.45\displaystyle P(A) = 0.45, P(B)=0.36\displaystyle P(B) = 0.36 and P(A∩B)=0.25\displaystyle P(A \cap B) = 0.25 then P(A/B)\displaystyle P(A/B) = ?
MCQ
3356
A husband and a wife appear in an interview for two vacancies in the same post. The probability of husband's selection is 3/5\displaystyle 3/5 and that of wife's selection is 1/5\displaystyle 1/5. Then the probability that only one of them is selected is
MCQ
3358
The odds in favor of event A\displaystyle A in a trial is 3:1\displaystyle 3:1. In three independent trials, the probability of non-occurrence of event A\displaystyle A is
MCQ
3359
Two events A\displaystyle A and B\displaystyle B are such that they do not occur simultaneously then they are called.
MCQ
3360
If P(A)=1/3\displaystyle P(A)=1/3, P(B)=3/4\displaystyle P(B)=3/4 and P(A∩B)=1/6\displaystyle P(A \cap B)=1/6 then P(A/B)\displaystyle P(A/B) is:
MCQ
3361
If a number is selected at random from the first 50\displaystyle 50 natural numbers, what will be the probability that the selected no. is a multiple of 3\displaystyle 3 and 4\displaystyle 4?
MCQ
3362
A number is selected at random from first 70\displaystyle 70 natural numbers. What is the chance that it is a multiple of either 5\displaystyle 5 or 14\displaystyle 14?
MCQ
3363
Probability of Ramesh & Deepak speaking truth is 1/4,3/5\displaystyle 1/4, 3/5. Find the probability of at most one of them speaks truth.
MCQ
3364
Three identical dice are rolled. The probability that the same number will appear on each of them is:
MCQ
3372
In connection with random experiment, it is found that P(A)=2/3\displaystyle P(A) = 2/3, P(B)=3/5\displaystyle P(B) = 3/5 and P(A∪B)=5/6\displaystyle P(A \cup B) = 5/6. Find P(A′/B)\displaystyle P(A'/B)
MCQ
3365
If 10\displaystyle 10 men, among whom are A\displaystyle A and B\displaystyle B, stand in a row, what is the probability that there will be exactly 3\displaystyle 3 men between A\displaystyle A and B\displaystyle B ?
MCQ
3366
The odds in favour of A\displaystyle A solving a problem is 5:7\displaystyle 5:7 and odds against B\displaystyle B solving the same problem is 9:6\displaystyle 9:6. What is the probability that if both of them try, the problem will be solved?
MCQ
3367
Ram is known to hit a target in 2\displaystyle 2 out of 3\displaystyle 3 shots whereas Shyam is known to hit the same target in 5\displaystyle 5 out of 11\displaystyle 11 shots. What is the probability that the target would be hit if they both try.
MCQ
3368
If P(A)=12\displaystyle P(A) = \frac{1}{2}, P(B)=13\displaystyle P(B) = \frac{1}{3} and P(A∩B)=14\displaystyle P(A \cap B) = \frac{1}{4} then the value of P(A∩B)\displaystyle P(A \cap B) is
MCQ
3369
In a box carrying one dozen of oranges, one third has become bad. If 3\displaystyle 3 oranges are taken out from the box at random, what is the probability that at least one orange out of the three oranges picked up is good?
MCQ
3370
One Card is drawn from pack of 52\displaystyle 52, what is the probability that it is a king or a queen?
MCQ
3371
If two letters are taken at random from the word HOME, what is the Probability that none of the letters would be vowels?
MCQ
3373
If a card is drawn at random from a pack of 52\displaystyle 52 cards, what is the chance of getting spade or an ace?
MCQ
3374
A number is selected at random from the set 1,2,...,99\displaystyle {1, 2, ..., 99}. The probability that it is divisible by 9\displaystyle 9 or 11\displaystyle 11 is
MCQ
3375
For two events A\displaystyle A and B\displaystyle B, P(A∪B)=P(A)+P(B)\displaystyle P(A \cup B) = P(A) + P(B) only when
MCQ
3376
An investment consultant predicts that the odds against the price of a certain stock going up are 2:1\displaystyle 2:1 and odd are in favor of the price remaining the same are 1:3\displaystyle 1:3. What is the probability that the price of stock will go down?
MCQ
3377
A pair of dice rolled. If the sum of the two dice is 9\displaystyle 9, find the prob. that one of the dice showed is 3\displaystyle 3.
MCQ
3378
What is the probability that a leap year selected at random contains either 53\displaystyle 53 Sundays or 53\displaystyle 53 Mondays.
MCQ
3379
The odds are 9:5\displaystyle 9:5 against a person who is 50\displaystyle 50 years living till he is 70\displaystyle 70 and 8:6\displaystyle 8:6 against a person who is 60\displaystyle 60 living till he is 80\displaystyle 80. Find the probability that at least one of them will be alive after 20\displaystyle 20 years.
MCQ
3387
Given that for two events A and B, P(A)=35\displaystyle P(A) = \frac{3}{5}, P(B)=23\displaystyle P(B) = \frac{2}{3} and P(A)=34\displaystyle P(A) = \frac{3}{4}, what is P(A/B)\displaystyle P(A/B)?
MCQ
3380
What is the chance of throwing at least 7\displaystyle 7 in a single cast with two dices?
MCQ
3381
A bag contains 12\displaystyle 12 balls of which 3\displaystyle 3 are red and 5\displaystyle 5 balls are drawn at random. Find the probability that 3\displaystyle 3 balls are red.
MCQ
3382
A bag contains 4\displaystyle 4 Red and 5\displaystyle 5 Black balls. Another bag contains 5\displaystyle 5 Red and 3\displaystyle 3 Black balls. If one ball is drawn at random each bag. Then the probability that one red and one black is
MCQ
3383
Given that for two events A and B, P(A)=35\displaystyle P(A) = \frac{3}{5}, P(B)=23\displaystyle P(B) = \frac{2}{3} and P(A∪B)=34\displaystyle P(A \cup B) = \frac{3}{4}, what is P(A/B)\displaystyle P(A/B)?
MCQ
3384
A problem in probability was given to three CA students A, B and C whose chances of solving it are 13\displaystyle \frac{1}{3}, 14\displaystyle \frac{1}{4} and 15\displaystyle \frac{1}{5} respectively. What is the probability that the problem would be solved?
MCQ
3385
A packet of 10\displaystyle 10 electronic components is known to include 2\displaystyle 2 defectives. If a sample of 4\displaystyle 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1\displaystyle 1 defective?
MCQ
3386
The probability that there is at least one error in an account statement prepared by 3\displaystyle 3 persons A, B and C are 0.2\displaystyle 0.2, 0.3\displaystyle 0.3 and 0.1\displaystyle 0.1 respectively. If A, B and C prepare 60\displaystyle 60, 70\displaystyle 70 and 90\displaystyle 90 such statements, then the expected number of correct statements
MCQ
3389
A bag contains 5\displaystyle 5 Red and 4\displaystyle 4 Black balls. A ball is drawn at random from the box and put into another bag contains 3\displaystyle 3 red and 6\displaystyle 6 black balls. A ball is drawn randomly from the second bag. What is the probability that it is red?
MCQ
3390
A speaks truth in 60%\displaystyle 60\% of the cases and B in 90%\displaystyle 90\% of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact:
MCQ
3391
Two events A\displaystyle A and B\displaystyle B are such that they do not occur simultaneously then they are called ______ events.
MCQ
3392
A bag contains 8 red and 5 white balls. Two successive draws of 3 balls are made without replacement. The prob. that the first draw will produce 3 white ball and second 3 red balls is :
MCQ
3393
If two events A\displaystyle A and B\displaystyle B are independent, the probability that both will occur is given by
MCQ
3395
Variance of a random variable x\displaystyle x is given by
MCQ
3396
If two random variables x\displaystyle x and y\displaystyle y are related by y=2−3x\displaystyle y = 2 - 3x, then the SD of y\displaystyle y is
MCQ
3397
If y≥x\displaystyle y \ge x, then mathematical expectation is
MCQ
3398
The value of K\displaystyle K for the probability density function of a variable X\displaystyle X is equal to: | X | P(x) ||---|---|| 0 | 5k\displaystyle 5k || 1 | 3k\displaystyle 3k || 2 | 4k\displaystyle 4k || 3 | 6k\displaystyle 6k || 4 | 7k\displaystyle 7k || 5 | 9k\displaystyle 9k || 6 | 11k\displaystyle 11k |
MCQ
3399
Assume that the probability for rain on a day is 0.4\displaystyle 0.4. An umbrella salesman can earn Rs 400\displaystyle \text{Rs } 400 per day in case of rain on that day and will lose Rs 100\displaystyle \text{Rs } 100 per day if there is no rain. The expected earnings in (in Rs \displaystyle \text{Rs }) per day of the salesman is
MCQ
3401
An unbiased coin is tossed 6\displaystyle 6 times. Find the probability that the tosses result in heads only,
MCQ
3403
A bag contains 6\displaystyle 6 white and 4\displaystyle 4 red balls. If a person draws 2\displaystyle 2 balls and receives 10\displaystyle 10 and 20\displaystyle 20 for a white and red balls respectively, then his expected amount is
MCQ
3404
Let X\displaystyle X be a random variable with the following distributionX | -2 | 4 | 8P(X) | 16\displaystyle \frac{1}{6} | 13\displaystyle \frac{1}{3} | 12\displaystyle \frac{1}{2}Find expected value of the random variable
MCQ
3405
For a probability of a random variable X\displaystyle X is given belowX | 1 | 2 | 4 | 5 | 6Y | 0.15 | 0.25 | 0.2 | 0.3 | 0.1What is The Standard deviation of X\displaystyle X?
MCQ
3406
In a business venture, a man can make a profit of 50,000\displaystyle 50,000 or incur a loss of 20,000\displaystyle 20,000. The probabilities of making profit or incurring loss, from the past experience, are known to be 0.75\displaystyle 0.75 and 0.25\displaystyle 0.25 respectively. What is his expected profit?
MCQ
3409
Four unbiased coins are tossed simultaneously. The expected number of heads is:X: | 0 | 1 | 2 | 3 | 4P(X) | 116\displaystyle \frac{1}{16} | 416\displaystyle \frac{4}{16} | 616\displaystyle \frac{6}{16} | 416\displaystyle \frac{4}{16} | 116\displaystyle \frac{1}{16}
MCQ
3410
If X\displaystyle X and Y\displaystyle Y are two random variables and if E(X)=3\displaystyle E(X) = 3 and E(Y)=6\displaystyle E(Y) = 6, then E(XY)\displaystyle E(XY) = ?
MCQ
3411
Assume that the probability for rain on a day is 0.4\displaystyle 0.4. An umbrella salesman can earn 400\displaystyle 400 per day in case of rain on that day will lose 100\displaystyle 100 per day if there is no rain . The expected earnings (in) per day of the salesman is
MCQ
3412
Probability distribution may be
MCQ

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