2017Math miscellaneousHard

Question

Let X and Y be two events such that P(X)=13, P(X|Y) = 12 and P(Y|X) = 25. Then

Options

A.

P(X|Y) = 12

B.

P(X∩Y) = 15

C.

P(X∪Y) = 25

D.

P(Y) = 415

Solution

P(XY) =P(X∩Y)P(Y)= 12P(YX) =P(X∩Y)P(X)= 25⇒P(X∩Y) =215P(Y)=415 also P(X∪Y) =715P(X'Y) = 1-P(XY) =1-12=12

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