Question

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

Moderate

Solution

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

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