A problem in probability was given to three CA students A, Band C whose chances of solving it are 1/3,1/5 and 1/2 respectively. What is the probability that the problem would be solved?

Correct Answer is : 111511/151511

Correct Answer is : 111511/151511

Test Index

Probability

Question : 76 of 127

Marks: +1, -0

A,

C

\frac{1}{3},\frac{1}{5}

\frac{1}{2}

Solution:

Concept:

Probability that the problem is solved = 1 minus probability that none solves it.

Explanation:

Chances of solving:

A: \frac{1}{3}, B: \frac{1}{5}, C: \frac{1}{2}

Probability that

A

does not solve:

1 - \frac{1}{3} = \frac{2}{3}

Probability that

B

does not solve:

1 - \frac{1}{5} = \frac{4}{5}

Probability that

C

does not solve:

1 - \frac{1}{2} = \frac{1}{2}

Assuming independence, probability that none solves:

\frac{2}{3} \times \frac{4}{5} \times \frac{1}{2} = \frac{8}{30} = \frac{4}{15}

Therefore, probability that the problem is solved:

1 - \frac{4}{15} = \frac{11}{15}

Answer:

\frac{11}{15}

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