If P(B) = 3/4, P(A ∩ B ∩ C) = 1/3 and P(A ∩ B ∩ C) = 1/3, then P(B ∩ C) is equal to

If P(B) = 3/4, P(A ∩ B ∩ C) = 1/3 and P(A ∩ B ∩ C) = 1/3,… — JEE Main 2002 Mathematics PYQ

AIEEE 2002

P(B) = \frac{3}{4}

P(A \cap B \cap \overline{C}) = \frac{1}{3}

and

P(\overline{A} \cap B \cap \overline{C}) = \frac{1}{3}

, then

P(B \cap C)

is equal to

Show answer and solution

Correct option: A

Solution

P(B) = P(B∩C) + P(B∩C̄)

P(B∩C̄) = P(A∩B∩C̄) + P(Ā∩B∩C̄) = 1/3 + 1/3 = 2/3

Therefore P(B∩C) = P(B) - P(B∩C̄) = 3/4 - 2/3 = 9/12 - 8/12 = 1/12.

[AIEEE 2002]

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