1. Suppose an urn has 5 blue balls and 8 red balls. Someone picks balls randomly from the urn with replacement where the replacement adds an extra ball of the same color. More specifically, each time a ball is drawn from the urn, it is returned to the urn along with an additional ball of the same color. Suppose three balls are drawn in this way.
1.a) Calculate the probability that all the three balls are blue.
1.b) Calculate the probability that only one ball, among the three balls, is blue.
1.c) Calculate the probability that the first ball drawn is a blue ball given that the second ball is blue. Assume that the third ball has not been drawn yet.
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