Question
Polya's urn. Suppose we have an urn containing one red ball and one blue ball. We draw a ball at random from the urn. If
Polya's urn. Suppose we have an urn containing one red ball and one blue ball. We draw a ball at random from the urn. If it is red, we put the drawn ball plus another red ball into the urn. If it is blue, we put the drawn ball plus another blue ball into the urn. We then repeat this process. At the n-th stage, we draw a ball at random from the urn with n + 1 balls, note its color, and put the drawn ball plus another ball of the same color into the urn.
(a) Find the probability that the first ball is red.
(b) Find the probability that the second ball is red.
(c) Find the probability that the first three balls are all red. (d) Find the probability that two of the first three balls are red.
Polya's um. Suppose we have an urn containing one red ball and one blue ball. We draw a ball at random from the urn. If it is red, we put the drawn ball plus another red ball into the urn. If it is blue, we put the drawn ball plus another blue ball into the urn. We then repeat this process. At the nth stage, we draw a ball at random from the urn with n + 1 balls, note its color, and put the drawn ball plus another ball of the same color into the urn. (a) Find the probability that the rst ball is red. (b) Find the probability that the second ball is red. (c) Find the probability that the first three balls are all red. (d) Find the probability that two of the first three balls are redStep by Step Solution
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