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JEE Advanced2017MathematicsProbabilityActual

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

Options

  1. AP Y = 4 15
  2. BP X ¯ | Y = 1 2
  3. CP X ∩ Y = 1 5
  4. DP X ∪ Y = 2 5

Correct answer

A. P Y = 4 15

Step-by-step solution

Using formula P X | Y = P ( X ∩ Y ) P ( Y ) and P Y | X = P ( Y ∩ X ) P ( X ) P X = 1 3 ; P X ∩ Y P Y = 1 2 ; P Y ∩ X P X = 2 5 From this information, we get P X ∩ Y = 2 15 ; P Y = 4 15 Using formula P ( X ∪ Y ) = P ( X ) + P ( Y ) − P ( X ∩ Y ) ∴ P X ∪ Y = 1 3 + 4 15 - 2 15 = 7 15 P X ¯ | Y = P X - ∩ Y P Y = P Y - P X ∩ Y P Y ⇒ P X ¯ | Y = 1 - 2 15 4 15 = 1 2

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