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Question
If P(A) = 0.5, P(B) = 0.8 and P(B/A) = 0.8, find P(A/B) and P(A ∪ B)
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Solution
Given P(A) = 0.5
P(B) = 0.8
and P(B/A) = 0.8
P(A/B) = `("P"("A" ∩ "B"))/("P"("B"))` .........(1)
P(B/A) = `("P"("B" ∩ "A"))/("P"("A"))`
P(A ∩ B) = P(B/A) P(A)
Substituting in equation (1) we get
(1) ⇒ P(A/B) = `("P"("B"/"A") * "p"("A"))/("P"("B"))`
= `(0.8 xx 0.5)/0.8`
P(A/B) = 0.5
P(A ∪ B) = P(A) + P(B) – P(A ∩ B) .........(2)
We have P(A/B) = `("P"("A" ∩ "B"))/("P"("B"))`
P(A ∩ B) = P(A/B) . P(B)
= 0.5 × 0.8
P(A ∩ B) = 0.40
(2) ⇒ P(A ∪ B) = 0.5 + 0.8 – 0.40
= 1.3 – 0.40
P(A ∪ B) = 0.90
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