If A and B are independent events such that P(A) = p, p(B) = 2p and P (Exactly one of A and B occurs) = 5/9, find the value of p.

Question

Philoid · Accepted Answer

Given P(A)=p and P(B)=2p

P(exactly one of A and B occurs)= P(A)P(+P(P(B)

⇒27p-36p² -5=0

⇒36p² -27p+5=0

⇒36p² -12p-15p+5=0

⇒12p(3p-1)-5(3p-1)=0

⇒ (12p-5)(3p-1)=0

⇒12p-5=0

also, 3p-1=0

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