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(C) Let $A, B, C$ be the events that the three students solve the question respectively.Given odds against are $2:1, 5:2, 5:3$.Therefore,the probabili

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$\frac{25}{56}$

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(C) Let $A, B, C$ be the events that the three students solve the question respectively.Given odds against are $2:1, 5:2, 5:3$.Therefore,the probabilities of solving the question are:$P(A) = \frac{1}{1+2} = \frac{1}{3}$,$P(\bar{A}) = \frac{2}{3}$$P(B) = \frac{2}{2+5} = \frac{2}{7}$,$P(\bar{B}) = \frac{5}{7}$$P(C) = \frac{3}{3+5} = \frac{3}{8}$,$P(\bar{C}) = \frac{5}{8}$The probability that the question is solved by only one student is given by:$P = P(A \cap \bar{B} \cap \bar{C}) + P(\bar{A} \cap B \cap \bar{C}) + P(\bar{A} \cap \bar{B} \cap C)$$P = (\frac{1}{3} 	imes \frac{5}{7} 	imes \frac{5}{8}) + (\frac{2}{3} 	imes \frac{2}{7} 	imes \frac{5}{8}) + (\frac{2}{3} 	imes \frac{5}{7} 	imes \frac{3}{8})$$P = \frac{25}{168} + \frac{20}{168} + \frac{30}{168}$$P = \frac{75}{168} = \frac{25}{56}$.

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

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