Compute P(Bag B | red) via Bayes

Q: Compute P(Bag B | red) via Bayes

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Question

Bayes' Rule: Posterior Probability of the Chosen Bag

Setup

There are three bags containing red (r) and green (g) balls:
- Bag A: 4 r, 6 g (10 total)
- Bag B: 6 r, 4 g (10 total)
- Bag C: 3 r, 7 g (10 total)
Process: Pick a bag at random, then draw one ball from that bag.
Event R: the drawn ball is red.

Tasks

With a uniform prior over bags (P(A)=P(B)=P(C)=1/3), compute P(B | R) using Bayes’ rule. Show all steps.
Follow-up: If instead P(A)=0.2, P(B)=0.5, P(C)=0.3, recompute P(B | R). Explain the intuition for how changing the prior affects the result.

Assume a single draw from the selected bag (replacement does not matter when drawing only once).

Compute P(Bag B | red) via Bayes

Bayes' Rule: Posterior Probability of the Chosen Bag

Setup

Tasks

Solution (Locked)

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