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

Engineering

Mathematics

Conditional Probability

Question

31 / 56

24 / 56

25 / 56

none of these

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Given,

P (A) = \frac{1}{3}, P (B) = \frac{2}{7}, P (C) = \frac{3}{8}

Probability that the question is solved only by one student is

= P(A) × P(B)^C × P(C)^C + P(A)^C × P(B) × P(C)^C + P(A)^C × P(B)^C × P(C)

= (\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}{56}

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