Maharashtra State BoardHSC Science (General) 11th
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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).

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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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