+117 Complete the two-way frequency table below, which shows the relationship between a person's gender and whether he or she wears his or her favorite sports team's jersey to sporting events. From a sample of 70 people entering a sports venue, it is found that there are 26 females, 45 people wearing a team jersey, and 17 females not wearing a team jersey.
Team Jersey No Team JerseyTotal
Female 17 26
Male
Total 45 70
What is the probability (rounded to the nearest whole percent) that a person entering a sports venue will be a male given that he or she is wearing a team jersey? Are the events being male and wearing a team jersey independent?
80%; they are independent
80%; they are not independent
82%; they are not independent
51%; they are independent
+129852 Team Jersey No Team JerseyTotal
Female 9 17 26
Male 36 8 44
Total 45 25 70
Probabilty that a person is male given that they are wearing a team jersey =
36/45 = 4/5 = .80 = 80%
To test whether this is independent
Let A = probability of being a male = 44/70
Let B = probability of wearing a team jersey = 45/70
P(A ∩ B) = P(A) x P(B) ???
.80 = (44/70) * (45/70) ??
.80 = .404 not independent
