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If X and Y are two independent even...

If X and Y are two independent events such that P(X)=18 and P(XY)=58, find P(Y).

A.

16

B.

47

C.

421

D.

37

Correct answer is B

P(XY)=58

P(XY)=P(X)×P(Y)

Since X and Y are independent events, the probability of their union (X ⋃ Y) can be calculated as:

P(XY)=P(X)+P(Y)P(XY)

=58=18+P(Y)18×P(Y)

=5818=P(Y)18×P(Y)

=12=P(Y)(118)

=12=P(Y)(78)

=P(Y)=12÷78

∴P(Y)=\frac{1}{2}x\frac{8}{7}=\frac{4}{7}