# For two events A and B of a sample space S, if P(A ∪ B) = 56, P(A ∩ B) = 13 and P(B') = 13, then find P(A). - Mathematics and Statistics

Sum

For two events A and B of a sample space S, if P(A ∪ B) = 5/6, P(A ∩ B) = 1/3 and P(B') = 1/3, then find P(A).

#### Solution

Here, P(A ∪ B) = 5/6, P(A ∩ B) = 1/3 and P(B') = 1/3

P(B') = 1/3

P(B) = 1 – P(B')

= 1 - 1/3

= 2/3

Since P(A ∪ B) = P(A) + P(B) – P(A ∩ B),

5/6 = "P"("A") + 2/3 - 1/3

∴ 5/6 = "P"("A") + 1/3

∴ P(A) = 5/6 - 1/3

= 1/2

Concept: Multiplication Theorem on Probability
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