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

Let P(A)=x and P(B)=y. Since A and B are  independent events, P(A∩B)=2/15⇒    P(A)P(B)=2/15⇒    (1−P(A))P(B)=2/15⇒    (1−x)y=2/15----1 and P(A∩B)=16⇒P(A)P(B)=16⇒ x(1−y)=16⇒ x−xy=16----2Subtracting (1) from (2), we getx−y=130⇒x=130+yPutting this value of x in (1), we get    y−y130+y=215⇒30y−y−30y2=2/5⇒     30y2−29y+4=0⇒(6y−1)(5y−4)=0⇒     y=1/6 or y=4/5⇒P(B)=1/16 or P(B)=4/5