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If P(A) = 14, P(B) = 25 and P(A ∪ B) = 12 Find the value of the following probability: P(A ∩ B') - Mathematics and Statistics

Sum

If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A ∩ B')

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Solution

Here, P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2`

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
∴ P(A ∩ B) = P(A) + P(B) − P(A ∪ B)
= `1/4+2/5-1/2`
= `3/20`
P(A ∩ B') = P(A) – P(A ∩ B)

= `1/4 - 3/20`

= `2/20`

= `1/10`

Concept: Addition Theorem of Probability
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