A and B are two independent events.The probability that both A and B occur is 1/6 and the probability that neither of them occurs is 1/3.Then the probability of the two events are respectively:

Explanation

Given: Probability that both occur simultaneously `= P(A) cdot P(B)=frac{1}{6}`,


Given: Probability that neither occur `= P(bar{A}) cdot P(bar{B})=frac{1}{3}.`


Hence, ` [1-P(A)][1-P(B)]=frac{1}{3}`


Assume `P(A)=x and P(B)=y`


`Rightarrow (1-x)(1-y)=frac{1}{3} and x y=frac{1}{6}`


`Rightarrow 1-x-y+x y=frac{1}{3} and x y=frac{1}{6}`


`Rightarrow x+y=frac{5}{6} and x y=frac{1}{6}`


`Rightarrow xleft(frac{5}{6}-xright)=frac{1}{6}`


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