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Complete the two-way frequency table below, which shows the relationship between student gender in a particular class and whether students wear jeans. From a sample of 30 students, it is found that there are 18 females, 20 people in the class who are wearing jeans, and 5 females not wearing jeans.

               Jeans   No Jeans   Total
Female                     5             18
Total          20                          30

What is the probability (rounded to the nearest whole percent) that a student will be a female given that he or she wears jeans? Are the events being female and wearing jeans independent?
A:43%; they are not independent
B:65%; they are not independent
C:72%; they are independent
D:65%; they are independent

 Apr 23, 2018

Some information is missing in the two-way frequency table, but it is still possible to determine the missing information. 


We know that there are 18 females in total. 5 females out of the 18 do not wear jeans. This means that 13 females wear jeans. We can use this information to figure out how many men wear jeans. 


We do not know how many men wear jeans in this sample. We do know, however, that 20 people, male or female, wear jeans. As aforementioned in the previous paragraph, 13 females wear jeans, so this leaves 7 men who wear jeans. We have gathered the information we have needed to figure out this problem. 


In summary, we know the following information:

  • 13 females wear jeans
  • 7 men wear jeans
  • 20 people, male of female, wear jeans in total

Therefore, \(\frac{13}{20}=\frac{65}{100}=65\%\) of people that wear jeans are female. Notice how the rest of the information in the table was superfluous and irrelevant to the question at hand. We did not care about the other information because the problem stated that we, the answerers, are only concerned with those who wear jeans. 

 Apr 24, 2018

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