If a and b are two mutually exclusive and exhaustive events and p(a)=2p(b), then p(b) is equal to:

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