Kelsey is a very consistent if mediocre golfer. On par three holes, they always

Question

Kelsey is a very consistent if mediocre golfer. On par three holes, they always score a four. Their friend, Kristin, is an erratic golfer. On par three holes, Kristin scores a three 70% of the time, and scores a six 30% of the time.

(a) What is the probability Kristin is ahead (smaller score) after 3 par three holes? What is the probability they tie?

(b) What is the probability Kristin is ahead (smaller score) after 4 par three holes?

(c) What are Kelsey and Kristin’s expected scores on a par three hole?

(d) Who do you think will win if they play a lot of par three holes in a row?

Explanation / Answer

a. After 3 par three holes, Kelsey's score = 4*3 = 12

P(Kristin is ahead) = P(Kristin's score <12) = P(Score of 3 in all 3 par three holes) = 0.7 * 0.7 * 0.7 = 0.343

P(They tie) = P(Kristin's score = 12) = P(2 scores of 3 and 1 score of 6) = 3C1 * 0.3 * 0.72 = 0.441

b. After 4 par three holes, Kelsey's score = 4*4 = 16

P(Kristin is ahead) = P(3 scores of 3 and 1 score of 6) + P(all scores of 3) = 4C1 * 0.3 * 0.73 + 0.74 = 0.6517

c. E[Kelsey's score] = 1*4 = 4

E[Kristin's score] = 0.7*3 + 0.3*6 = 3.9

d. As E[Kristin's score] < E[Kelsey's score], Kristin will win if they play a lot of par three holes in a row.

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