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Question
The odds against student X solving a statistics problem are 8:6 and odds in favour of student y solving the same problem are 14:16. Find is the chance that neither of them solves the problem
Solution
The odds against X solving a problem are 8:6.
Let P(X') = P(X does not solve the problem)
= `8/(8 + 6)`
= `8/14`
So, the probability that X solves the problem
= P(X)
= 1 – P(X')
= `1 - 8/14`
= `6/14`
Similarly, let P(Y) = P(Y solves the problem) Since odds in favour of Y solving the problem are 14:16,
P(Y) = `14/(14 + 16)`
= `14/30`
So, the probability that Y does not solve the problem
= P(Y')
= 1 – P(Y)
= `1 - 14/30`
= `16/30`
Required probability = P(X' ∩ Y')
Since X and Y are independent events, X' and Y' are also independent events.
∴ Required probability = P(X').P(Y')
= `8/14 xx 16/30`
= `32/105`
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