Assume that a bag initially contains 6 balls: 2 red, 2 green and 2 blue balls....

Assume that a bag initially contains 6 balls: 2 red, 2 green and 2 blue balls. At each step, you choose a ball from the bag at random, note its color, but do not put it back into the bag. Instead, you add to the bag two balls, which are of of two different colors, and different in color from the color of the removed ball. (For example, if you choose a red ball in the first step, then after the first step the bag will contain one red, three green and three blue balls.)

(a) Compute the probability that in the first three steps, the selected balls are, in order, red, green and blue.

(b) Compute the probability that the balls selected on 2nd and 3rd step are, in order, green and blue

(c) Compute the conditional probability that the ball selected in the first step is red, given that the balls selected on 2nd and 3rd step are, in order, green, and blue

(d) Compute the probability that the two balls selected on 2nd and 3rd step are of different colors.

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