12 Exercise 6189 Algorithmic The prior probabilities of even

12. Exercise 6.189 (Algorithmic) The prior probabilities of events A1, A2, and A3 are P(A1) = 0.52, P(A2) = 0.15 and P(A3) = 0.33. The conditional probabilities of event B given A2, and 43 are P(B | A1) = 0.38, P(B | A2) = 0.55 and P(B | A3) = 0.27. (Round your answer(s) to 3 decimal places.) Compute P(B and A2) =

Solution

Using definition of condition probabiity for any two events A and B, P(A|B) = P(A and B)/P(B)

P(A and B) = P(A|B)*P(B)

Hence for given case,

P(B and A₂) = P(B|A₂)*P(A₂)

= 0.55*0.15

P(B and A₂)  = 0.0825