Question

A survey has 989 respondents, 759 male and 230 female. out of 989 respondents, 196 attended multiple football games. of these 196 fans that attended multiple games, 177 were male. a. what is probability that a randomly selected fan has attended multiple games. b. given 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 attended multiple games.

Answer 1

a.
The total number attending multiple football games is 196. The total number of respondents is 989 (all assumed to be fans). Therefore the probability that a randomly selected fan has attended multiple games is given by:
\[\frac{196}{989}=you\ can\ calculate\]

Answer 2

Define events
M=male
F=female
MG=attended multiple games

(a)
P(MG)=196/989 as @kropot72 indicated earlier.
(c) intersection of two sets
\(P(M\cap MG)=177/989 \) since there are only 177 males who attended multiple games.
(b) review conditional probability
\(P(A|B)=P(A\cap B)/P(B)\) probability of A happening when B has already happened.
\(P(M|MG)=P(M\cap MG)/P(MG)=(177/989)/(196/989)=?\)
(d)
\(P(MG|M)=P(MG\cap M)/P(M)=(177/989)/(759/989)=?\)