Assume that there are 6 different issues of Newsweek magazine, 7 different issues of Sports Illustrated, and 4 different issues of Time, including the December 1st issue, on a rack.

Question

Assume that there are 6 different issues of Newsweek magazine, 7 different issues of Sports Illustrated, and 4 different issues of Time, including the December 1st issue, on a rack. You choose 4 of them at random.

(1) What is the probability that exactly 3 are issues issue of Newsweek? 

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

Answer 1

1) P(selecting 3 Newsweek out of 4 selections when there are 6 Newsweeks and 6+7+4 = 17 total, is

C(6,3)C(17-6,4-3)/C(17,4) =

20*11/2380 = 11/119

You can get this on your calculator or in Excel using the hpergeometric distribution (P 3 successes of 4 when 6 successes of 17) = in Excel hypgeom.dist(3,4,6,17,0) = 11/119 (Use the fraction format with 3 digits in the denominator).

2) As you are choosing 4 magazines, and there are 17 total, the probability of selecting a particular magazine is 4 * 1/17 = 4/17