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14. probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS14. probability1 Mark
MCQ
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
  • A
    $\frac{{31}}{{56}}$
  • B
    $\frac{{24}}{{56}}$
  • ✓
    $\frac{{25}}{{56}}$
  • D
    None of these
✓

Answer

Correct option: C.
$\frac{{25}}{{56}}$
c
(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}}$.

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