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Question
If for two events A and B, P(A) = `3/4`, P(B) = `2/5` and A ∪ B = S (sample space), find the conditional probability P(A/B)
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Solution
Given P(A) = `3/4`
P(B) = `2/5`
A ∪ B = S
n(A ∪ B) = n(S)
P(A ∪ B) = `("n"("A" ∪ "B"))/("n"("S"))`
P(A ∪ B) = `("n"("S"))/("n"("S"))` = 1
P(A/B) = `("n"("A" ∩ "B"))/("P"("B"))`
= `("P"("A") + "P"("B") - "P"("A" ∪ "B"))/("P"("B"))`
= `(3/4 + 28/5 - 1)/(2/5)`
= `((15 + 8 - 20)/20)/(2/5)`
= `(23 - 20)/20 xx 5/2`
P(A/B) = `3/20 xx 5/2`
= `3/8`
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