Conditional probability · Lucky draw
The rich get richer
A box holds 2 red and 3 blue balls. Each round you draw one ball uniformly at random, note its color, and put it back together with one extra ball of the same color, so whatever is drawn becomes more likely next time. The first draw is red. Given that, what is the probability that draw number 5 is red?
Answer with a probability. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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