PR1005 Pr204 and PR3055 Also PQ R1 07 PQ R2 03 and P Q R3

P(R₁)=0.05, P(r₂)₌0.4, and P(R₃)=0.55. Also, P(Q | R₁ )=0.7, P(Q | R₂)= 0.3, and P (Q | R₃ )= 0.4. Find P(R₁ | Q).

Solution

P(R1|Q) = P(Q and R1)/(P(Q and R1) + P(Q and R2) + P(Q and R3))

P(Q and Rn) = P(Q|Rn)*P(Rn) ... for n=1, 2, 3.

P(R1 | Q) = (0.05*0.7)/((0.7)(0.05) + (0.5)(0.4) + (0.8)(0.55))
= .035/(.035 + 0.20 + 0.44)
= .035/.675 = 0.05185