A problem of mathematics is given to three students whose chances of solving problem are frac{{1}}{{

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14.Probability

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A problem of mathematics is given to three students whose chances of solving the problem are $\frac{{1}}{{3}} , \frac{{1}}{{4}}$ and $\frac{{1}}{{5}}$ respectively. The probability that the question will be solved is

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{4}{5}$

$\frac{3}{5}$

Solution

(d) The probability of students not solving the problem are $1 – \frac{1}{3} = \frac{2}{3},$ $1 – \frac{1}{4} = \frac{3}{4}$ and $1 – \frac{1}{5} = \frac{4}{5}$

Therefore the probability that the problem is not solved by any one of them $ = \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} = \frac{2}{5}$

Hence the probability that problem is solved$ = 1 – \frac{2}{5} = \frac{3}{5}$.

Standard 11

Mathematics

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easy

(IIT-1979)

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hard

(JEE MAIN-2023)

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A problem of mathematics is given to three students whose chances of solving the problem are $\frac{{1}}{{3}} , \frac{{1}}{{4}}$ and $\frac{{1}}{{5}}$ respectively. The probability that the question will be solved is

Solution

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