If A and B are two events such that P ( A ¯ ) = 0 . 3 , P B = 0 . 4 and P A ∩ B ¯ = 0 . 5 , then P B ∣ A ∪ B ¯ =

Question

If A and B are two events such that P ( A ¯ ) = 0 . 3 , P B = 0 . 4 and P A ∩ B ¯ = 0 . 5 , then P B ∣ A ∪ B ¯ =, 0 . 3, 0 . 1, 0 . 25, 0 . 75

MARKS App · Accepted Answer

Here, P A ∪ B ¯ = P A + P B ¯ - P A ∩ B ¯ ⇒ P A ∪ B ¯ = 0 . 7 + 0 . 6 - 0 . 5 = 0 . 8 ⇒ 1 - P B + P A ∪ B = 0 . 8 ⇒ P A ∪ B = 0 . 2 Now, P B ∣ A ∪ B ¯ = P B ∩ ( A ∪ B ¯ ) P A ∪ B ¯ ⇒ P B ∣ A ∪ B ¯ = P B ∩ A P A ∪ B ¯ ⇒ P B ∣ A ∪ B ¯ = 0 . 2 0 . 8 = 0 . 25

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