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Given two events A and B . If odds again...

Given two events `A` and `B` . If odds against `A` are as 2:1 and those in favour of `AuuB` are 3:1, then find the range of `P(B)`.

Text Solution

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Clearly P(A) = `1//3`, `P(A uu B) = 3//4`. Now,
`P(B) le P(A uu B)`
`implies P(B) le 3//4 " "(1)`
Also, P(B) = `P(A uu B) - P(A) + P(A nn B) ge (3)/(4) - (1)/(3) = (5)/(12)` Hence, `(5)/(12) le P(B) le (3)/(4)`
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