4.

We have P (B) = p, P (Ac|B) = q, and P (Ac Bc) = r. Compute the following: (a) P (A|B) Hint: Use properties of conditional probabilities (in p66 of the Ch.2 lecture note) (b) P (A B) (c) P (Ac B) Hint: Use (b) and Question 2-(c). (d) P (A B) Hint: Use P (Ac Bc) = r . (e) P (A) Hint: Use P (A B) = P (A) + P (B) P (A B). (f) P (B|A)