JIPMAT 2023 (QA) - <p>The probabilities that A, B, and D can solve a problem independently are 1/3, 1/3, and 1/4 respectively. The probability that only two of them are able to solve the problem is:</p> | PYQs + Solutions

JIPMAT 2023

Modern Math

Probability

Easy

The probabilities that A, B, and D can solve a problem independently are 1/3, 1/3, and 1/4 respectively. The probability that only two of them are able to solve the problem is:

\frac{5}{36}

\frac{7}{36}

\frac{13}{36}

\frac12

Correct Option: 2

1) Let's first identify given probabilities:

\newline

P(A) = \frac{1}{3}

P(B) = \frac{1}{3}

P(D) = \frac{1}{4}

2) For only two of them to solve:

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We need to find:

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P(\text{AB but not D}) + P(\text{AD but not B}) + P(\text{BD but not A})

3) For AB but not D:

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P(A) × P(B) × (1-P(D))

\frac{1}{3} × \frac{1}{3} × \frac{3}{4}

\frac{1}{12}

4) For AD but not B:

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P(A) × P(D) × (1-P(B))

\frac{1}{3} × \frac{1}{4} × \frac{2}{3}

\frac{1}{18}

5) For BD but not A:

\newline

P(B) × P(D) × (1-P(A))

\frac{1}{3} × \frac{1}{4} × \frac{2}{3}

\frac{1}{18}

6) Total probability:

\frac{1}{12} + \frac{1}{18} + \frac{1}{18}

\frac{3}{36} + \frac{2}{36} + \frac{2}{36}

\frac{7}{36}

Therefore, the probability is

\frac{7}{36}