Professors at the University of Chicago and the University of Pennsylvania analyzed 1,613,234 putts by golfers on the Professional Golfers Association (PGA) Tour and found that 983,764 putts were made and 629,470 putts were missed (Is Tiger Woods Loss Averse? Persistent Bias in the Face of Experience, Competition, and high Stakes, American Economic Review, February, 2011)

a. What is the probability that a PGA Tour player makes a putt? What is the probability that a PGA Tour player misses a putt?

b. Suppose that a PGA Tour player has a par putt. It is known that of putts made, 64.0% were for par while for putts missed, 20.3% were for par. What is the revised probability of making a putt given the PGA Tour player has a par putt?

c. A birdie occurs when a player makes a putt in one stroke less than par. Suppose that a PGA Tour player has a birdie putt. It is known that of putts made, 18.8% were for birdie whereas for putts missed, 73.4% were for birdie. What is the revised probability of making a putt given the PGA Tour player has a birdie putt?

d. Comment on the differences in the probabilities computed in parts (b) and (c).