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Bags hold 2, 3, 4, 5, 6 candies and each is taken with probability 1/2: what is the probability of taking at least half of all candies?

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Five bags hold 2, 3, 4, 5 and 6 candies. Charlie decides separately for each bag, on a fair coin flip, whether to take it. What is the probability he ends up with at least half of all the candies?

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