1.

A and B are two mutually exclusive and exhaustive events of a random experiment such that `P(A)=6[P(B)]^2` where P(A) and P(B) denotes probability of A and B respectively. Find P(A) and P(B)

Answer» As, `A` and `B` are mutually exahaustive events,
`:. A uu B = S`
`:.P(AuuB) = P(S) = 1`
As, `A` and `B` are mutually exclusive events,
`:. P(AuuB) = P(A)+P(B)`.
`=>P(A)+P(B) = 1`
`=>6P(B)^2+P(B) - 1 = 0`...(Given that `P(A) = 6P(B)^2`)
`=>6P(B)^2+3P(B)-2P(B) - 1 = 0`
`=>3P(B)(2P(B)+1)-1(2P(B)+1) = 0`
`=>(3P(B)-1)(2P(B)+1) = 0`
`=>P(B) = 1/3 and P(B) = -1/2`
As, `P(B)` can not be negative, so, `P(B) = 1/3`
`:. P(A) = 6(1/3)^2 = 2/3.`


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