439.Rigging the Candy Boxes
★★★conditional probabilityCh. 2 — Axiomatic and Conditional Probability444+ Problems in Probability
You have 5 good candies, 5 bad candies, and two boxes. You may distribute all 10 candies between the boxes however you like. Your blindfolded brother then picks a box uniformly at random and draws one candy uniformly at random from it, which you receive. Playing optimally, what is the probability you receive a good candy?
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Make one box as pure as possible while keeping the other box as good as possible.
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