If odds against solving a question by three s | vedclass

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Question

(c) The probability of solving the question by these three students are $\frac{1}{3},\frac{2}{7}$ and $\frac{3}{8}$ respectively.

$P(A) = \frac{1}{

Vedclass · Accepted Answer

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

Vedclass · Answer

(c) The probability of solving the question by these three students are $\frac{1}{3},\frac{2}{7}$ and $\frac{3}{8}$ respectively.

$P(A) = \frac{1}{3}$; $P(B) = \frac{2}{7}$; $P(C) = \frac{3}{8}$

Then probability of question solved by only one student

$ = P(A\,\bar B\,\bar C\,$ or $\bar A\,B\,\bar C$ or $\bar A\,\bar B\,C)$

$ = P(A)\,\,P(\bar B)\,\,P(\bar C)\, + \,P(\bar A)\,\,P(B)\,P(\bar C)\, + \,\,P(\bar A)\,P(\bar B)\,P\,(C)$

$ = \frac{1}{3}.\frac{5}{7}.\frac{5}{8} + \frac{2}{3}.\frac{2}{7}.\frac{5}{8} + \frac{2}{3}.\frac{5}{7}.\frac{3}{8}$

$ = \frac{{25 + 20 + 30}}{{168}}$$ = \frac{{25}}{{56}}$.

If odds against solving a question by three students are $2 : 1 , 5:2$ and $5:3$ respectively, then probability that the question is solved only by one student is

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