Question

Assume that there are 8 different issues of Sports Illustrated magazine, 7 different issues of Newsweek, and 3 different issues of Time, including the December 1st issue, on a rack. You choose 4 of them at random. What is the probability that exactly 3 are issues of Sports Illustrated?

A) 0.17
B) 0.15
C) 0.20
D) 0.25

Answer 1

The probability of selecting exactly 3 issues of Sports Illustrated is found by combining combinations for selecting magazines and dividing by the total number of ways to select 4 magazines. The closest answer is 0.17, option A.

Step-by-step explanation:

To find the probability of selecting exactly 3 issues of Sports Illustrated from the given magazines, we need to use the concept of combinations. We have 8 issues of Sports Illustrated, 7 of Newsweek, and 3 of Time. We want to choose 4 magazines such that 3 are Sports Illustrated and 1 is from the remaining magazines (Newsweek or Time).

First, we calculate the number of ways to select 3 issues of Sports Illustrated, which is a combination of 3 from 8: C(8,3). Then, we calculate the ways to select 1 issue from the remaining magazines which is a combination of 1 from 10 (7 Newsweek + 3 Time): C(10,1).

The total number of ways to select 4 magazines from all 18 is C(18,4).

The probability is then calculated as follows:

(C(8,3) * C(10,1)) / C(18,4).

Plugging the numbers into the formula:

(C(8,3) * C(10,1)) / C(18,4) = (56 * 10) / 3060 = 560 / 3060 = 28 / 153 ≈ 0.183

Looking at the options given, the closest is option A) 0.17.