For two events A and B of a sample space S, if P(A) =38, P(B) = 12 and P(A ∪ B) = 58. Find the value of the following: P(A ∩ B) - Mathematics and Statistics

Sum

For two events A and B of a sample space S, if P(A) = 3/8, P(B) = 1/2 and P(A ∪ B) = 5/8. Find the value of the following: P(A ∩ B)

Solution

It is given that,

P(A) = 3/8, P(B) = 1/2 and P(A ∪ B) = 5/8.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

∴ 5/8 = 3/8 + 1/2 - "P"("A" ∩ "B")

∴ P(A ∩ B) = 3/8 + 1/2 - 5/8

= 2/8

= 1/4

Concept: Multiplication Theorem on Probability
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