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14.Probability
medium
Three persons work independently on a problem. If the respective probabilities that they will solve it are $\frac{{1}}{{3}} , \frac{{1}}{{4}}$ and $\frac{{1}}{{5}}$, then the probability that none can solve it
A
$\frac{2}{5}$
B
$\frac{3}{5}$
C
$\frac{1}{3}$
D
None of these
Solution
(a) Required probability $ = \left( {1 – \frac{1}{3}} \right){\rm{ }}\left( {1 – \frac{1}{4}} \right){\rm{ }}\left( {1 – \frac{1}{5}} \right)$
$ = \frac{2}{3}.\frac{3}{4}.\frac{4}{5} = \frac{2}{5}.$
Standard 11
Mathematics
