Hello, Hasnain!

I assume you're familiar with Bayes' Theorem: .Two events and are such that: .

Find: .

(a) We have: .

Since and

. . the equation becomes: .

Therefore: .

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(b) There are a number of ways to determine

Here's one of them . . .

We are given: .

Since , then

. . and the equation becomes: .

Sketching a Venn diagram, we see that:

. .

. . .

Then: .

Hence: .

Therefore: .

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(c) We've done the hard work ... This part is easy . . .