Let X and Y be two events such that P X = 1 3 , P X Y = 1 2 and P Y | X = 2 5 . Then

Let X and Y be two events such that PX=13, PXY=12 and PY|X=25. Then
  1. PY=415
  2. P X ¯ | Y=12
  3. PX∩Y=15
  4. PX∪Y=25

Solution

Using formula PX | Y= P( X∩Y ) P( Y )  and PY | X= P( Y∩X ) P( X )
PX=13;PX∩YPY=12;PY∩XPX=25
From this information, we get
PX∩Y=215;PY=415
Using formula P(X∪Y)=P(X)+P(Y)−P(X∩Y)
∴   PX∪Y=13+415-215=715
P X ¯ | Y=PX-∩YPY=PY-PX∩YPY
⇒     P X ¯ | Y=1-215415=12

Asked in: JEE Advanced 2017 (Paper 1)

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