A problem of Mathematics is given to three students, whose chances of solving it are What is the probability that the problem will be solved? - Wired Faculty

Probability

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A problem of Mathematics is given to three students, whose chances of solving it are $1 third comma space 1 fourth comma space 1 fifth.$ What is the probability that the problem will be solved?

Solution

The probabilities of three students solving the problem are $1 third comma space 1 fourth comma space 1 fifth$ respectively.
$therefore$ proabilites of three students not solving the problem are
$1 minus 1 third space equals 2 over 3 comma space space 1 minus 1 fourth space equals 3 over 4 comma space space 1 minus 1 fifth space equals 4 over 5 space respectively.$
$therefore$ the probability that the problem is not solved by any one of them
$equals space 2 over 3 cross times 3 over 4 cross times 4 over 5 space equals 2 over 5$
$therefore$ probability that the problem will be solved by atleast one of them
$equals space 1 minus 2 over 5 space equals space 3 over 5$

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Probability

A problem of Mathematics is given to three students, whose chances of solving it are $1 third comma space 1 fourth comma space 1 fifth.$ What is the probability that the problem will be solved?

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