If A and B are two independent events such that `P(overline(A) cap B)=2//15 " and " P(A cap overline(B))=1//6`, then P(B), is

Question

If A and B are two independent events such that P( ˉ A ∩B)=2/15 and P(A∩ ˉ B )=1/6, then P(B), is A. 1 5 or , 4 5 B. 1 6 or, 5 6 C. 4 5 or, 1 6 D. 5 6 or, 1 5 Select the correct answer from above options

Answer 1

Correct Answer - C Let P(A)=x and P(B)=y. Since A and B are independent events. Therefore, P( ˉ A ∩B)=2/15 ⇒P( ˉ A )P(B)=2/15 ⇒{1-P(A)}P(B)=2/15 ⇒(1-x)y=2/15 ⇒y=xy=2/15 and, P(A∩ ˉ B )= 1 6 ⇒P(A)P( ˉ B )= 1 6 ⇒x(1-y)= 1 6 ⇒x-xy= 1 6 Subtracting (i) from (ii), we get x-y= 1 30 ⇒x= 1 30 +y Putting this value of x in (i), we get y-y( 1 30 +y)= 2 15 ⇒30y-y-30y2=4 ⇒30y2-29y+4=0 ⇒(6y-1)(5y-4)=0⇒y=1/6 or ,y=4/5 ∴P(B)=1/6 or ,P(B)=4/5