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Question
Three events A, B and C have probabilities `2/5, 1/3` and `1/2`, , respectively. Given that P(A ∩ C) = `1/5` and P(B ∩ C) = `1/4`, find the values of P(C|B) and P(A' ∩ C').
Solution
We have P(A) =`2/5`
P(B) = `1/3`
And PC) = `1/2`
P(A ∩ C) = `1/5` and P(B ∩ C) = `1/4`
∴ `"P"("C"/"B") = ("P"("B" ∩ "C"))/("P"("B"))`
= `(1/4)/(1/3)`
= `3/4`
P(A' ∩ C') = 1 – P(A ∪ C)
= 1 – [P(A) + P(C) – P(A ∩ C)]
= `1 - [2/5 + 1/2 - 1/5]`
= `1 - 7/10`
= `3/10`
Hence, the required probabilities are `3/4` and `3/10`.
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