Probability

According to bayee's theorem, $P(E_i / A) = \frac{P(E_i)P(A / E_i)}{\sum_{j=1}^{n} P(E_j)P(A / E_j)}$ here

When $2$ - dice are thrown simultaneously then the probability of getting at least one $5$ is

A log contains $15$ one rupee coins, $25$ two rupees coins and $10$ five rupee coins if a coin is selected at random than probability for not selecting a one rupee coin is:

What is the probability of occurring $4$ or more than $4$ accidents.No. of acc. | Frequency0 | 361 | 272 | 233 | 244 | 245 | 276 | 187 | 9

When two coins are tossed simultaneously the probability of getting at least one tail?

Two broad divisions of probability are

The term "chance" and probability are synonyms:

Sum of all probabilities mutually exclusive and exhaustive events is equal to

The probability that a leap year has $53$ Wednesday is

Two different dice are thrown simultaneously, then the probability that the sum of two numbers appearing on the top of dice is $9$ is:

Two event $A$ and $B$ are such that they do not occurs simultaneously then they are called events

When $3$ dice are rolled simultaneously the probability of a number on the $3^{rd}$ dice is greater than the sum of the numbers on two dice.

An event that can be subdivided into further events is called as.

Three identical and balanced dice are rolled. The probability that the same number will appear on each of them is.

A basket contains $15$ white balls, $25$ red balls and $10$ blue balls. If a ball is selected at random, the probability of selecting not a white ball.

Two dice are thrown simultaneously. The probability of a total score of $5$ from the out comes of dice is.

If an unbiased coin is tossed onece, then the probability of obtaining at least one tail is.

If an unbiased coin is tossed three times, what is the probability of getting more than one head?

Which of the following pair of events $E$ and $F$ are mutually exclusive?

What is the probability of occurrence of leap year having $53$ Sunday?

Two perfect dice are rolled what is the probability that one appears at least in one of the dice?

If $p, q$ are the odds in favour of an event, then the probability of that event is -

The probability that a leap year has $53$ Monday is:

If a number is selected at random from the first $50$ natural numbers, what will be the probability that the selected number is a multiple of $3$ and $4$?

If three coins are tossed simultaneously, what is the probability of getting two heads together?

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

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.

If a card is drawn at random from a pack of 52 cards, what is the chance of getting a Club or a King?

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?

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?

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:

If $P: Q$ is the odds in favor of an event, then the probability of that event is

If $P(A) = \frac{4}{9}$, then odd against the event 'A' is

The probability of A solving a problem is $\frac{7}{12}$ odds against solving a problem

When $2$ dice are thrown simultaneously then the probability of getting at least one $5$ is:

The probability that a leap year has $53$ Wednesday is:

Ticket number $1$ to $20$ 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 $3$ or $7$?

The probability that a leap year has $53$ Sunday is:

If a card is drawn randomly from a deck, the probability of the card being neither a red card nor a face card?

If two dice are thrown then what is the probability that the sum of the faces of dice are square or cube number?

If a card is drawn at random from a pack of cards, what is the chance of getting spade or an ace?

The chance of getting a sum of $10$ in a simple single throw is

Exactly $3$ girls are to be selected from $5$ girls and $3$ boys. The probability of selecting $3$ girls will be

A bag contains $15$ one rupee coins, $25$ two rupee coins and $10$ five rupee coins. If a coin is selected at random from the bag, then the probability of not selecting a one rupee coin is:

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

If $P(A) = 4:9$, then odd against the event 'A' is

If $p:q$ is the odds in favor of an event, then the probability of that event is -

There are two boxes containing $5$ white and $6$ blue balls and $3$ white and $4$ 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

A box contains $5$ white and $7$ black balls. Two successive drawn of $3$ 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.

$X$ and $Y$ are stand in a line with $6$ people. What is the probability that there are three persons between them?

Ram is known to hit a target in $2$ out of $3$ shots where as Shyam is known to hit the same target in $5$ out of $11$ shots. What is the probability that the target would be hit if they both try?

If $P(A \cup B) = 0.8$ and $P(A \cap B) = 0.3$, then $P(A) + P(B)$ is equal to

If a coin is tossed $5$ times then the probability of getting Tail and Head occurs alternatively is

Two letters are chosen from the word HOME. What is the probability that the letters chosen are not vowels.

If $A, B, C$ are three mutually exclusive and exhaustive events such that: $P(A) = 2P(B) = 3P(C)$ what is $P(B)$?

What is the probability of having at least one '$6$' in $3$ throws of a project die?

If $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$ then $P(A \cup B)$ is equal to

A coin is tossed six times, then the probability of obtaining heads and tails alternatively is

What is the probability of getting $7$ or $11$ when two dice are thrown?

When $2$ fair dice are thrown, what is the probability of getting the sum which is a multiple of $3$?

If $A$ speaks $75\%$ of truth and $B$ speaks $60\%$ of truth. In what percentage both of them likely contradict with each other in narrating the same questions?

If there are $48$ marbles market with numbers $1$ to $48$, then the probability of selecting a marble having the number divisible by $4$ is;

A bag contains $7$ blue and $5$ green balls. One ball is drawn at random. The probability of getting a blue ball is_______.

The probability that a football team loosing a match at Kolkata is $3/5$ and winning a match at Bengaluru is $6/7$; the probability of the team winning at least one match is

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 $4$ times, what is the probability of getting a head all the times?

If there are $16$ phones, $10$ of them are Android and $6$ of them Apple, then the probability of $4$ randomly selected phones to include $2$ Android and $2$ Apple phone is:

A dice is rolled twice. Find the probability of getting numbers multiple of $3$ or $5$?

If in a bag of $30$ balls numbered from $1$ to $30$. Two balls are drawn find probability of getting a ball being multiple of $2$ or $3$

If $P(A) = 0.3$; $P(B) = 0.8$ and $P\left(\frac{B}{A}\right) = 0.5$, find $P(A \cup B)$

If $P(A) = \frac{1}{3}$, $P(B) = \frac{3}{4}$ and $P(A \cap B) = \frac{11}{12}$ then $P\left(\frac{B}{A}\right)$ is:

For any two events 'A' and 'B' it is known that $P(A) = 2/3$, $P(B) = 3/8$ and $P(A \cap B) = 1/4$, then the events A and B are:

The probability that a four digit number comprising the digits $2, 5, 6$ and $7$ without repetition of digits, would be divisible by $4$ is

If $P(A) = 1/2$ and $P(B) = 1/3$ and $P(A \cap B) = 2/3$ then find $P(A \cap B)$

A number is selected from the first $30$ natural numbers. What is the probability that it would be divisible by $3$ or $8$?

If $P(A \cap B) = \frac{1}{3}$, $P(A \cup B) = \frac{5}{6}$ $P(B) = \frac{2}{3}$ then $P(\bar{A})$ is:

A number is selected at random from the first $100$ natural numbers. What is the probability that it would be a multiple of $3$ or $7$?

A number is selected at random from the set $\{1, 2, \dots, 99\}$. The probability that it is divisible by $9$ or $11$ is

A question in statistics is given to three students A, B and C. Their chances of solving the question are $1/3, 1/5$ and $1/7$ respectively. The probability that the question would be solved is

A company produces two types of products, A and B. The probability of defective product in type A is $0.05$ and in type B is $0.03$. If the company produces $60\%$ type A and $40\%$ type B, what is the probability of a randomly selected product being defective?

Which one holds correct for any two events A and B?

Which of the following pairs of events are mutually exclusive?

The probability of success of three students in CA Foundation examination are $1/5, 1/4$ and $1/3$ respectively. Find the probability that at least two students will get success.

If $P(A) = 0.65$ and $P(B) = 0.15$, then $P(A) + P(B)$ is:

Two events A&B Probabilities $0.24$ and $0.52$ respectively. If the probability of both A and B occurs simultaneously is $0.15$. Then the probability that neither A nor B occur is $0.15$, then the probabilities that neither A nor B is.

If $P(A \cap B)=0$, then the two events $A$ and $B$ are

If $A, B$ and $C$ are mutually exclusive and exhaustive events, then $P(A) + P(B) + P(C)$ equals to

Addition Theorem of Probability states that for any two events $A$ and $B$

Three events $A, B$ and $C$ are mutually exclusive, exhaustive and equally likely. What is the probability of the complementary event of $A$?

Find the probability that a four-digit number comprising the digits $2, 5, 6$ and $7$ would be divisible by $4$.

If $A$ and $B$ are two events such that $P(A) = 1/4$, $P(B) = 1/3$ and $P(A \cup B) = 1/2$, then $P(B/A)$ is equal to

If $A$ and $B$ are two events and $P(A) = 2/3$, $P(B) = 3/5$, $P(A \cup B) = 5/6$, then the value of $P(A'/B')$ is :

$P(A) = 0.45$, $P(B) = 0.36$ and $P(A \cap B) = 0.25$ then $P(A/B)$ = ?

A husband and a wife appear in an interview for two vacancies in the same post. The probability of husband's selection is $3/5$ and that of wife's selection is $1/5$. Then the probability that only one of them is selected is

Thirty balls are serially numbered and placed in bag. Find chance that the first ball drawn is a multiple of $3$ or $5$

The odds in favor of event $A$ in a trial is $3:1$. In three independent trials, the probability of non-occurrence of event $A$ is

Two events $A$ and $B$ are such that they do not occur simultaneously then they are called.

If $P(A)=1/3$, $P(B)=3/4$ and $P(A \cap B)=1/6$ then $P(A/B)$ is:

If a number is selected at random from the first $50$ natural numbers, what will be the probability that the selected no. is a multiple of $3$ and $4$?

A number is selected at random from first $70$ natural numbers. What is the chance that it is a multiple of either $5$ or $14$?

Probability of Ramesh & Deepak speaking truth is $1/4, 3/5$. Find the probability of at most one of them speaks truth.

Three identical dice are rolled. The probability that the same number will appear on each of them is:

If $10$ men, among whom are $A$ and $B$, stand in a row, what is the probability that there will be exactly $3$ men between $A$ and $B$ ?

The odds in favour of $A$ solving a problem is $5:7$ and odds against $B$ solving the same problem is $9:6$. What is the probability that if both of them try, the problem will be solved?

Ram is known to hit a target in $2$ out of $3$ shots whereas Shyam is known to hit the same target in $5$ out of $11$ shots. What is the probability that the target would be hit if they both try.

If $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$ then the value of $P(A \cap B)$ is

In a box carrying one dozen of oranges, one third has become bad. If $3$ 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?

One Card is drawn from pack of $52$, what is the probability that it is a king or a queen?

If two letters are taken at random from the word HOME, what is the Probability that none of the letters would be vowels?

In connection with random experiment, it is found that $P(A) = 2/3$, $P(B) = 3/5$ and $P(A \cup B) = 5/6$. Find $P(A'/B)$

If a card is drawn at random from a pack of $52$ cards, what is the chance of getting spade or an ace?

A number is selected at random from the set ${1, 2, ..., 99}$. The probability that it is divisible by $9$ or $11$ is

For two events $A$ and $B$, $P(A \cup B) = P(A) + P(B)$ only when

An investment consultant predicts that the odds against the price of a certain stock going up are $2:1$ and odd are in favor of the price remaining the same are $1:3$. What is the probability that the price of stock will go down?

A pair of dice rolled. If the sum of the two dice is $9$, find the prob. that one of the dice showed is $3$.

What is the probability that a leap year selected at random contains either $53$ Sundays or $53$ Mondays.

The odds are $9:5$ against a person who is $50$ years living till he is $70$ and $8:6$ against a person who is $60$ living till he is $80$. Find the probability that at least one of them will be alive after $20$ years.

What is the chance of throwing at least $7$ in a single cast with two dices?

A bag contains $12$ balls of which $3$ are red and $5$ balls are drawn at random. Find the probability that $3$ balls are red.

A bag contains $4$ Red and $5$ Black balls. Another bag contains $5$ Red and $3$ Black balls. If one ball is drawn at random each bag. Then the probability that one red and one black is

Given that for two events A and B, $P(A) = \frac{3}{5}$, $P(B) = \frac{2}{3}$ and $P(A \cup B) = \frac{3}{4}$, what is $P(A/B)$?

A problem in probability was given to three CA students A, B and C whose chances of solving it are $\frac{1}{3}$, $\frac{1}{4}$ and $\frac{1}{5}$ respectively. What is the probability that the problem would be solved?

A packet of $10$ electronic components is known to include $2$ defectives. If a sample of $4$ components is selected at random from the packet, what is the probability that the sample does not contain more than $1$ defective?

The probability that there is at least one error in an account statement prepared by $3$ persons A, B and C are $0.2$, $0.3$ and $0.1$ respectively. If A, B and C prepare $60$, $70$ and $90$ such statements, then the expected number of correct statements

Given that for two events A and B, $P(A) = \frac{3}{5}$, $P(B) = \frac{2}{3}$ and $P(A) = \frac{3}{4}$, what is $P(A/B)$?

If $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$, $P(A \cap B) = \frac{1}{4}$, then the value of $P(A' \cup B')$ is

A bag contains $5$ Red and $4$ Black balls. A ball is drawn at random from the box and put into another bag contains $3$ red and $6$ black balls. A ball is drawn randomly from the second bag. What is the probability that it is red?

A speaks truth in $60\%$ of the cases and B in $90\%$ of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact:

Two events $A$ and $B$ are such that they do not occur simultaneously then they are called ______ events.

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 :

If two events $A$ and $B$ are independent, the probability that both will occur is given by

If $P(A) = \frac{1}{2}$, $P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$, what is $P(A/B)$?

Variance of a random variable $x$ is given by

If two random variables $x$ and $y$ are related by $y = 2 - 3x$, then the SD of $y$ is

If $y \ge x$, then mathematical expectation is

The value of $K$ for the probability density function of a variable $X$ is equal to: | X | P(x) ||---|---|| 0 | $5k$ || 1 | $3k$ || 2 | $4k$ || 3 | $6k$ || 4 | $7k$ || 5 | $9k$ || 6 | $11k$ |

Assume that the probability for rain on a day is $0.4$. An umbrella salesman can earn $\text{Rs } 400$ per day in case of rain on that day and will lose $\text{Rs } 100$ per day if there is no rain. The expected earnings in (in $\text{Rs }$) per day of the salesman is

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

An unbiased coin is tossed $6$ times. Find the probability that the tosses result in heads only,

If a random variable $X$ assumes the values $x_1, x_2, x_3, x_4$ with corresponding probabilities, $P_1, P_2, P_3, P_4$ then the expected value of $X$ is

A bag contains $6$ white and $4$ red balls. If a person draws $2$ balls and receives $10$ and $20$ for a white and red balls respectively, then his expected amount is

Let $X$ be a random variable with the following distributionX | -2 | 4 | 8P(X) | $\frac{1}{6}$ | $\frac{1}{3}$ | $\frac{1}{2}$Find expected value of the random variable

For a probability of a random variable $X$ is given belowX | 1 | 2 | 4 | 5 | 6Y | 0.15 | 0.25 | 0.2 | 0.3 | 0.1What is The Standard deviation of $X$?

In a business venture, a man can make a profit of $50,000$ or incur a loss of $20,000$. The probabilities of making profit or incurring loss, from the past experience, are known to be $0.75$ and $0.25$ respectively. What is his expected profit?

If $2x + 3y - 4 = 0$ and $V(x) = 6$ then $V(y)$ is

From the following probability distribution table, find $E(x)$:X | 1 | 2 | 3f(X) | $\frac{1}{2}$ | $\frac{1}{3}$ | $\frac{1}{6}$

Four unbiased coins are tossed simultaneously. The expected number of heads is:X: | 0 | 1 | 2 | 3 | 4P(X) | $\frac{1}{16}$ | $\frac{4}{16}$ | $\frac{6}{16}$ | $\frac{4}{16}$ | $\frac{1}{16}$

If $X$ and $Y$ are two random variables and if $E(X) = 3$ and $E(Y) = 6$, then $E(XY)$ = ?

Assume that the probability for rain on a day is $0.4$. An umbrella salesman can earn $400$ per day in case of rain on that day will lose $100$ per day if there is no rain . The expected earnings (in) per day of the salesman is

Probability distribution may be