ProbabilityMCQMTP Dec 2023 Series IQuestion 2830 of 295
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If P(A∩B)=0.10\displaystyle P(A \cap B) = 0.10, and P(B′)=0.80\displaystyle P(B') = 0.80, then P(A/B)\displaystyle P(A/B) is

Options

A11\displaystyle 11
B6\displaystyle 6
C5\displaystyle 5
D9\displaystyle 9
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Correct Answer

✅ Option a — 11\displaystyle 11

All Options:

  • A11\displaystyle 11
  • B6\displaystyle 6
  • C5\displaystyle 5
  • D9\displaystyle 9

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Detailed Solution & Explanation

We are given: - P(A∩B)=0.10\displaystyle P(A \cap B) = 0.10 - P(B′)=0.80\displaystyle P(B') = 0.80 First, calculate the probability of event B\displaystyle B, P(B)\displaystyle P(B): P(B)=1−P(B′)=1−0.80=0.20\displaystyle P(B) = 1 - P(B') = 1 - 0.80 = 0.20. Next, find the conditional probability P(A/B)\displaystyle P(A/B): P(A/B)=P(A∩B)P(B)=0.100.20=12=0.5\displaystyle P(A/B) = \frac{P(A \cap B)}{P(B)} = \frac{0.10}{0.20} = \frac{1}{2} = 0.5. Let us match this result with the options. The options are 11\displaystyle 11, 6\displaystyle 6, 5\displaystyle 5, and 9\displaystyle 9. This indicates a typographical error where fractions or decimals have been parsed with deleted slashes and decimals: - Option A is "11\displaystyle 11", which corresponds to "1/2\displaystyle 1/2" (the slash "/" was parsed as "1", converting "1/2" to "11"). - Option B is "6\displaystyle 6", which corresponds to "1/6\displaystyle 1/6". - Option C is "5\displaystyle 5", which corresponds to "1/5\displaystyle 1/5". - Option D is "9\displaystyle 9", which corresponds to "1/9\displaystyle 1/9". Since the correct answer is 1/2\displaystyle 1/2, it corresponds to Option A (typographically parsed as 11\displaystyle 11). Hence, **Option A** 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.

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