Assume that there are 5 different issues of Sports Illustrated magazine, 6 different issues of Time, and 4 different issues of Newsweek, including the December 1st issue, on a rack

Question

You choose 4 of them at random.

(1) What is the probability that exactly 2 are issues issue of Sports Illustrated?

(2) What is the probability that you choose the December 1st issue of Newsweek?

Answer 1

(1) To choose exactly 2 issues of Sports Illustrated, we can use combinations. The number of ways to choose 2 issues out of 5 is C(5,2) = 10. The total number of ways to choose 4 magazines out of 15 (5 Sports Illustrated + 6 Time + 4 Newsweek) is C(15,4) = 3005. Therefore, the probability of choosing exactly 2 issues of Sports Illustrated is 10/3005 = 1/301.

(2) To choose the December 1st issue of Newsweek, we need to choose 3 other magazines out of 14 (the December 1st issue of Newsweek is excluded). The number of ways to do this is C(14,3) = 364. The total number of ways to choose 4 magazines out of 15 (5 Sports Illustrated + 6 Time + 4 Newsweek) is C(15,4) = 3005. Therefore, the probability of choosing the December 1st issue of Newsweek is 364/3005 = 12/101.