If P(A) = 1 and P(B) = 1/3 then P(A/B) =

Option c: 1. Solution: By the definition of conditional probability: P(A/B) = P(A B)/P(B) 1. We are given P(A) = 1 , which means A is a sure event. 2. Since P(A) = 1 , the complement event A' has probability P(A') = 0 . 3. We can write event B as a union of two mutually exclusive events: B = (B A) (B A') 4. Taking probabilities on both sides: P(B) = P(B A) + P(B A') 5. Since B A' A' , we have P(B A') ≤ P(A') = 0 , so P(B A') = 0 . 6. Thus, P(A B) = P(B) . 7. Substituting this back into the conditional probability formula: P(A/B) = P(B)/P(B) = 1 Hence, Option C is the correct answer.

ProbabilityMCQMTP Nov 18Question 2816 of 295

All Questions

If $\displaystyle P(A) = 1$ and $\displaystyle P(B) = \frac{1}{3}$ then $\displaystyle P(A/B) =$

Options

\displaystyle \frac{1}{3}

\displaystyle \frac{2}{3}

\displaystyle \frac{1}{2}

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 1

All Options:

A $\displaystyle \frac{1}{3}$
B $\displaystyle \frac{2}{3}$
C1
D $\displaystyle \frac{1}{2}$

Detailed Solution & Explanation

By the definition of conditional probability:

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

1. We are given

\displaystyle P(A) = 1

, which means

\displaystyle A

is a sure event. 2. Since

\displaystyle P(A) = 1

, the complement event

\displaystyle A'

has probability

\displaystyle P(A') = 0

. 3. We can write event

\displaystyle B

as a union of two mutually exclusive events:

B = (B \cap A) \cup (B \cap A')

4. Taking probabilities on both sides:

P(B) = P(B \cap A) + P(B \cap A')

5. Since

\displaystyle B \cap A' \subseteq A'

, we have

\displaystyle P(B \cap A') \le P(A') = 0

, so

\displaystyle P(B \cap A') = 0

. 6. Thus,

\displaystyle P(A \cap B) = P(B)

. 7. Substituting this back into the conditional probability formula:

P(A/B) = \frac{P(B)}{P(B)} = 1

Hence, **Option C** 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.

View Official ICAI Syllabus

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.

Ready to Master Probability?

Practice all 295 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

If P(A)=1\displaystyle P(A) = 1P(A)=1 and P(B)=13\displaystyle P(B) = \frac{1}{3}P(B)=31​ then P(A/B)=\displaystyle P(A/B) =P(A/B)=