Assume that there are 7 different issues of Newsweek, 8 different issues of Time, and 4 different issues of Sports Illustrated, including the December 1st issue, on the rack. You choose 4 of them at random.
(1) What is the probability that you choose 2 issues of Newsweek and 2 issues of Time?
(2) What is the probability that you choose at least 1 of the Time magazines
1. 7 over 8
To calculate the probability of choosing certain combinations of magazines, we need to take into account the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. Since we are choosing 4 magazines out of a total of 7 Newsweek issues, 8 Time issues, and 4 Sports Illustrated issues, the total number of possible outcomes can be calculated using the combination formula (nCr). In this case, it is (7+8+4) C 4.
(1) To calculate the probability of choosing 2 issues of Newsweek and 2 issues of Time, we need to calculate the number of favorable outcomes. Since we want to choose 2 Newsweek issues out of 7 and 2 Time issues out of 8, we can calculate the number of favorable outcomes using the combination formula.
Number of favorable outcomes = (7 C 2) * (8 C 2)
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
(2) To calculate the probability of choosing at least 1 Time magazine, we can calculate the probability of not choosing any Time magazine and subtract it from 1.
Probability of not choosing any Time magazine:
Number of favorable outcomes = (7 C 4) + (4 C 4) (choosing only Newsweek and Sports Illustrated)
Probability = Number of favorable outcomes / Total number of possible outcomes
Finally, subtract the probability of not choosing any Time magazine from 1 to get the probability of choosing at least 1 Time magazine.
I hope this helps! Let me know if you have any further questions.