Compute P(Bag B | red) via Bayes

Three bags contain red (r) and green (g) balls: - Bag A: 4 r, 6 g - Bag B: 6 r, 4 g - Bag C: 3 r, 7 g Process: pick a bag uniformly at random, then draw one ball from that bag. Given the drawn ball is red, compute the posterior probability that it came from Bag B, i.e., P(B | red). Show all steps using Bayes’ rule. Follow-up: if instead the bag is chosen with probabilities P(A)=0.2, P(B)=0.5, P(C)=0.3, recompute P(B | red) and explain the intuition for how the prior changes the result.