Question

let a and b be two given independent events such that p(a)=p and p(b)=q and p (exactly one of A, B) then the value of 3p+3q-6pq is​

Answer 1

Given :  A and B be two given independent events such that P(A)=p and P(B)=q  

To Find : 3p+3q-6pq   in terms of P (exactly one of A, B)

Solution:

a and b  independent events

=>P(A ∩ B)  =P(A).P(B)

P (exactly one of A, B)  = P (only A)  + P ( only B)

= P(A) - P(A)P(B)  + P(B) - P(B)P(A)

= P(A) + P(B) - 2 P(A)P(B)

= p + q  - 2 pq

3p+3q-6pq  = 3(  p + q  - 2 pq)

=> 3p+3q-6pq  =  3  P (exactly one of A, B)

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