A golfer has a probability of (1 - 0.1n) of making an n-foot putt, where n is less than 10. He adopts the following routine for practicing putts from three to seven feet. He begins with a three foot putt. Anytime he makes a putt, he tries one which is a foot longer and any time he misses, he goes back to a foot shorter putt. If he misses on the three-foot putt or makes the seven-foot putt, he repeats that distance.
(a) If he continues his session for a very long time, what is the most likely distance that he will finish with? Estimate the probability of finishing at that distance.
(b) Repeat part (a) only assuming now that he is practicing putts from four to eight feet.