A Mathematics problem is given to two students X and Y to solve. The odds in favour of X solving the problem are 6 to 9 and the odds against Y in solving the problem are 6 to 5. What is the probability that the problem will be solved if both X and Y try to solve the problem?
\(\dfrac{37}{55}\)
The odds in favour of X give \(P(X) = \dfrac{6}{6+9} = \dfrac{2}{5}\), and the odds against Y give \(P(Y) = \dfrac{5}{6+5} = \dfrac{5}{11}\). The probability that the problem is solved by at least one of them is \(1-\left(1-\dfrac{2}{5}\right)\left(1-\dfrac{5}{11}\right) = 1-\dfrac{3}{5}\times\dfrac{6}{11} = 1-\dfrac{18}{55} = \dfrac{37}{55}\).
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