Question

Use thefollowing results from the 839 player challenges to referee calls in the first U.S. Open tennis tournament to use the Hawk-Eye electronic instant replay system.

	player challenge was accepted	player challenge was rejected
male players	201	288
female players	126	224

a. If two challenges are randomly selected with replacement, find the probability of selecting a challenge that was accepted followed by one that is rejected.

b. If two challenges are randomly selected without replacement, find the probability of selecting a challenge that was accepted followed by one that is rejected.

c. If three challenges are randomly selected with replacement, find the probability that they are all challenges that were accepted.

d. If three challenges are randomly selected without replacement, find the probability that they are all challenges that were accepted.

e. If one challenge is randomly selected, find the probability of getting a challenge that was made by a male player, given it was rejected.

f. If one challenge is randomly selected, find the probability of getting a challenge that was rejected, given it was made by a male player.

Answer 1

a) P(selecting a challenge that was accepted followed by one that is rejected, with replacement) = (201+126)/839 x (288+224)/839

= 0.2471

b) P(selecting a challenge that was accepted followed by one that is rejected, without replacement) = (201+126)/839 x (288+224)/838

= 0.2381

c) P(all three are accepted, with replacement) = [(201+126)/839]³

= 0.0592

d) P(all three are accepted, without replacement) = 327/839 x 326/838 x 325/837

= 0.0589

e) P(male | rejected) = 288/(288+224)

= 0.5625

f) P(rejected | male) = 288/(201+288)

= 0.5890