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PROBLEM 1. A box has a ball which is either red or black, with equal probabilities. Suppose we add a second red ball to the

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PROBLEM 1. A box has a ball which is either red or black, with equal probabilities. Suppose we add a second red ball to the box, and choose a ball uniformly at random. Given that the ball we chose is red, what is the probability that the remaining ball is also red

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