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').

Answer 1

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`.