Independent events A , B satisfy P ( A ∩ B ˉ ) = 1/3 and P ( A ∪ B ) = 11/15 . Find P ( A ∩ B ) .

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Independent events $A, B$ satisfy $P (A \cap \overset{ˉ}{B}) = 1/3$ and $P (A \cup B) = 11/15$ . Find $P (A \cap B)$ .

Answer:

Solution:

Let $P (A) = a, P (B) = b$ . Then $a (1 - b) = 1/3$ and $a + b - ab = 11/15$ . Hence $b = 2/5, a = 5/9$ , so $ab = 2/9$ .

Stream:JEESubject:MathematicsTopic:Probability

⏱ 2mℹ️ Source: QB

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