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14. probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS14. probability1 Mark
MCQ
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
  • ✓
    $\frac{2}{5}$
  • B
    $\frac{3}{5}$
  • C
    $\frac{1}{3}$
  • D
    None of these
✓

Answer

Correct option: A.
$\frac{2}{5}$
a
(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}.$

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