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Question
If A and B are two events associated with a random experiment such that P(A) = 0.3, P (B) = 0.4 and P (A ∪ B) = 0.5, find P (A ∩ B).
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Solution
Given:
P(A) = 0.3, P (B) = 0.4 and P (A ∪ B) = 0.5
By addition theorem, we have:
P (A ∪ B) = P(A) + P (B) - P (A ∩ B)
⇒ 0.5 = 0.3 + 0.4 -P (A ∩ B)
⇒ 0.5 = 0.7 - P (A ∩ B)
⇒ P (A ∩ B) = 0.7 - 0.5
= 0.2
Hence, P (A ∩ B) = 0.2
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