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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

failurewithasmile  Apr 15, 2017
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2+0 Answers

 #1
avatar+79894 
+2

 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

 

 

cool cool cool

CPhill  Apr 15, 2017
 #2
avatar+117 
0

Thank you, so what makes them not independent?

failurewithasmile  Apr 15, 2017

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