Question 764690: Consider a health club with 100 (60 men and 40 women). Each member uses the club for just one favorite activity, and men and women are equally likely to engage in any of the activities. Of the members of the club 20 swimmers; 30 play racquetball; 24 take aerobic exercise classes; 16 lift weights; and 10 play indoor tennis.
a. suppose a member of the club is randomly selected:
1. What is the probability that the member is either a tennis player, a racquetball player, or a weight lifter?
b. suppose that two members of the club are randomly selected:
1. What is the probability that both are tennis players?
Please help and explain. Not sure how to even approach problem.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 20 swimmers
30 racquetball
24 aerobic
16 weights
10 indoor tennis
total = 100
1. What is the probability that the member is either a tennis player, a racquetball player, or a weight lifter?
since a member is either a tennis player, a racquetball player, or a weight lifter, then no member does both or all 3 so the probability of tennis or racquetball or weight = 10/100 + 30/100 + 16/100 = 56/100.
there are 56 members who are either tennis player, racquetball player, or weight lifter. therefore you have 56 chances out of 100 that you will pick a member at random and that member will be one of that group.
b. suppose that two members of the club are randomly selected:
1. What is the probability that both are tennis players?
the probability that both will be tennis players will be 10/100 * 9/99 = 90/9900 = 9/990 = 1/110
you have 10 choices out of 100 for the first player you pick to be a tennis player and then you have 9 choices out of the remaining 99 players for the second player chosen to be a tennis player.
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