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Question
The odds that the event A occurs is 5 to 7, find P(A)
Solution
Given the odds, that event A occurs is 5 to 7.
∴ `("P"("A'"))/("P"("A")) = 7/5`
But P(A') = 1 – P(A)
∴ `(1 - "P"("A"))/("P"("A")) = 7/5`
`1/("P"("A")) - ("P"("A"))/("P"("A")) = 7/5`
`1/("P"("A")) - 1 = 7/5`
`1/("P"("A")) = 1 + 7/5`
= `(5 + 7)/5`
= `12/5`
∴ P(A) = `5/12`
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