Interested in learning more about its fans, the marketing office of the Arena Fo
ID: 394928 • Letter: I
Question
Interested in learning more about its fans, the marketing office of the Arena Football
League (AFL) conducted a survey at one of its games. The survey had 989 respondents,
759 males and 230 females. Out of the 989 total respondents, 196 stated that they had attended
multiple AFL games. Of these 196 fans that had attended multiple games, 177 were
male. Using this survey information, answer the following questions.
a. What is the probability that a randomly selected fan has attended multiple games?
b. Given that a randomly selected fan has attended multiple games, what is the probability
of this person being male?
c. What is the probability of a randomly selected fan being male and having attended
multiple games?
d. Given that a randomly selected fan is male, what is the probability that this person has
attended multiple games?
e. What is the probability that a randomly selected fan is male or has attended multiple
games?
Explanation / Answer
a.
(196/989) = 19.81%
i.e., number of respondents who said they attended multiple games divided by total number of survey respondents.
b.
(177/196) = 90.3%
i.e., number of males who said they attended multiple games divided by total number of survey respondents who have been to multiple games.
c.
number of males who said they attended multiple games divided by total number of survey respondents who are males = (177/759) = 25.82%
d.
Probability of being a male = (759/989) = 0.7674
Probability of having attended a multiple game = (196/989) = 0.1891
Total probability is 95.65%
e.
Total number of males divided by total number of survey respondents = 759/989 = 0.7674
Total number of survey respondents who said they attended multiple games divided by total number of survey respondents = 196/989 = 0.1891
Total probability is 95.65%
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