Question

The odds that the event A occurs is 5 to 7, find P(A)

Answer 1

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`