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14. probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS14. probability1 Mark
MCQ
The probability of $A, B, C$ solving a problem are $\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}$ respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is
  • A
    $\frac{{25}}{{168}}$
  • ✓
    $\frac{{25}}{{56}}$
  • C
    $\frac{{20}}{{168}}$
  • D
    $\frac{{30}}{{168}}$
✓

Answer

Correct option: B.
$\frac{{25}}{{56}}$
b
(b) Here ${p_1} = \frac{1}{3},$ ${p_2} = \frac{2}{7}$ and ${p_3} = \frac{3}{8}$

$ \Rightarrow {q_1} = \frac{2}{3},$ ${q_2} = \frac{5}{7}$ and ${q_3} = \frac{5}{8}$

Required probability $ = {p_1}{q_2}{q_3} - {q_1}{p_2}{q_3} + {q_1}{q_2}{p_3}.$

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