Question: Two Wharton professors analyzed 1,613,234 putts by golfers on the Professional Golfers Association (PGA) Tour and found that 983,764 of the putts were made and 629,470 of the putts were missed. Further analysis showed that for putts that were made, 64.0% of the time the player was attempting to make a par putt and 18.8% of the time the player was attempting to make a birdie putt. And, for puns that were missed, 20.3% of the time the player was attempting to make a par putt and 73.4% of the time the player was attempting to make a birdie putt (Is Tiger Woods Loss Averse? Persistent Bias in the Face of Experi-ence. Competition, and High Stakes. Pope, D. G.. and M. E. Schweitzer, June 2009. The Wharton School. University of Pennsylvania.).

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

b. Suppose that a PGA Tour player has a putt for par. What is the probability that the player will make the putt?

c. Suppose that a PGA Tour player has a putt for birdie. What is the probability that the player will make the putt?

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