Probability of A, B, C solving a problem are frac{1}{3},,frac{2}{7},,frac{3}{8} respectively. If all

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14.Probability

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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

$\frac{{25}}{{168}}$

B

$\frac{{25}}{{56}}$

C

$\frac{{20}}{{168}}$

D

$\frac{{30}}{{168}}$

Solution

(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}.$

Standard 11

Mathematics

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