A problem in statistics is given to $3$ students $A, B, C$ . This chances of solving problems are $1 / 3, 1 / 4$ and $1 / 5$ respectively. If all of $3$ try independently what is probability that exactly two students solve the problem.

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Solution

probability
$P_{1}$ = $\frac{1}{3} \times \frac{1}{4} \times (1 - \frac{1}{5})$
$P_{1} = \frac{1}{15}$
similarly,
$P_{2}$ = $\frac{1}{20}$
$P_{3} = \frac{1}{30}$
net probability = $P_{1} + P_{2} + P_{3} = \frac{9}{60}$

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