385.Bertrand's Bowls
★★★conditional probabilityCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
Three bowls: one holds two blue balls, one holds two red balls, one holds one of each. You pick a bowl uniformly at random and draw a ball — it's blue. You replace it and draw again from the same bowl. What is the probability the second draw is also blue?
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The first blue draw changes the odds of which bowl you're holding — update first, then predict.
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