The employment center at a university wanted to know the proportion of students

Question

The employment center at a university wanted to know the proportion of students who worked and also the proportion of those who lived in the dorm. The following data were collected: What is the probability of selecting a student at random who works either full or part time? What is the probability that a student who works lives in the dorm? What is the probability that a student either works full time or does not live in the dorm? Is the event that a student lives in the dorm independent of the event that a student works full time? Discuss what your answer means.

Explanation / Answer

a. P(full time or part time)=P(full time)+P(part time)-P(full time and part time) = ((19+25)+(22+9)-0)/100= 0.75

b. P(student works and lives in the dorm)=(19+22)/100 =0.41

c. P( works full time OR does not live in the dorm)=P(works full time)+P(does not live in dorm)-P( works full time AND does not live in dorm) =((19+25)+39-25)/100=0.58

d. P(works full time) =(19+25)/100 =0.44

P(lives in dorm)=0.61

P(student works full time AND lives in dorm)=0.19

since P(student works full time AND lives in dorm) not equal P(lives in dorm)*P(works full time)

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