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Question
Solve the following:
The odds against A solving a certain problem are 4 to 3 and the odds in favor of solving the same problem are 7 to 5 find the probability that the problem will be solved
Solution
Let J ≡ the event that John solves the problem
R ≡ the event that Rafi solves the problem
Odds against John solving the problem are 4 : 3
∴ P(J') = `4/(4 + 3) = 4/7`
∴ P(J) = 1 – P(J') = `3/7`
Odds in favour of Rafi solving the problem are 7 : 5
∴ P(R) = `7/(7 + 5) = 7/12`
∴ P(R') = 1 – P(R) = `5/12`
P(problem is solved) = 1 – P(problem is not solved)
= 1 – P(J' ∩ R')
= 1 – P(J')·P(R') ...[∵ events J' and R' are independent]
= `1 - 4/7*5/12`
= `1 - 5/21`
= `16/21`.
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