In connection with a random experiment, it is found that P(A) = 2/3 , P(B) = 3/5 and P(A B) = 5/6 , find P(A/B)

Option d: 13/18. Solution: We want to find P(A/B) , which is the conditional probability of A given B . 1. By conditional probability: P(A/B) = P(A B)/P(B) 2. Find P(A B) using the addition theorem of probability: P(A B) = P(A) + P(B) - P(A B) P(A B) = P(A) + P(B) - P(A B) 3. Substitute the given values: P(A B) = 2/3 + 3/5 - 5/6 4. Use a common denominator of 30: P(A B) = 20/30 + 18/30 - 25/30 = 13/30 5. Calculate P(A/B) : P(A/B) = 13/30/P(B) = 13/30/3/5 = 13/30 × 5/3 = 13/18 Hence, Option D is the correct answer.

ProbabilityMCQMTP May 20Question 2821 of 295

All Questions

In connection with a random experiment, it is found that $\displaystyle P(A) = \frac{2}{3}$ , $\displaystyle P(B) = \frac{3}{5}$ and $\displaystyle P(A \cup B) = \frac{5}{6}$ , find $\displaystyle P(A/B)$

Options

\displaystyle \frac{7}{18}

\displaystyle \frac{1}{13}

\displaystyle \frac{5}{18}

\displaystyle \frac{13}{18}

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Correct Answer

✅ Option d — $\displaystyle \frac{13}{18}$

All Options:

A $\displaystyle \frac{7}{18}$
B $\displaystyle \frac{1}{13}$
C $\displaystyle \frac{5}{18}$
D $\displaystyle \frac{13}{18}$

Detailed Solution & Explanation

We want to find

\displaystyle P(A/B)

, which is the conditional probability of

\displaystyle A

given

\displaystyle B

. 1. By conditional probability:

P(A/B) = \frac{P(A \cap B)}{P(B)}

2. Find

\displaystyle P(A \cap B)

using the addition theorem of probability:

P(A \cup B) = P(A) + P(B) - P(A \cap B)

P(A \cap B) = P(A) + P(B) - P(A \cup B)

3. Substitute the given values:

P(A \cap B) = \frac{2}{3} + \frac{3}{5} - \frac{5}{6}

4. Use a common denominator of 30:

P(A \cap B) = \frac{20}{30} + \frac{18}{30} - \frac{25}{30} = \frac{13}{30}

5. Calculate

\displaystyle P(A/B)

P(A/B) = \frac{13/30}{P(B)} = \frac{13/30}{3/5} = \frac{13}{30} \times \frac{5}{3} = \frac{13}{18}

Hence, **Option D** is the correct answer.

About This Chapter: Probability

Paper

Paper 3: Quantitative Aptitude

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.

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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.

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In connection with a random experiment, it is found that P(A)=23\displaystyle P(A) = \frac{2}{3}P(A)=32​, P(B)=35\displaystyle P(B) = \frac{3}{5}P(B)=53​ and P(A∪B)=56\displaystyle P(A \cup B) = \frac{5}{6}P(A∪B)=65​, find P(A/B)\displaystyle P(A/B)P(A/B)