4. (40 points). An urn always contains 2 balls, and ball colors are either red or blue. At each stage, a ball is randoml

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4 40 Points An Urn Always Contains 2 Balls And Ball Colors Are Either Red Or Blue At Each Stage A Ball Is Randoml 1 (37.79 KiB) Viewed 148 times

4. (40 points). An urn always contains 2 balls, and ball colors are either red or blue. At each stage, a ball is randomly chosen (i.e., each ball chosen with probability 0.5) and replaced by a new ball. The new ball is with probability 0.6 of the same color as the ball it replaces, and with probability 0.4 the opposite color as the ball it replaces. (a) [20 points) If initially both balls are red, find the probability that the fourth ball selected is blue. (b) (20 points) If you can not observe ball colors in the urn, find the probability that a blue ball is selected after a large number of selections.