c Does the choice of major affect the probability of a student living on campus or not?
A
a 13 %
B
b See solution.
C
c Yes, they are associated. See solution.
Practice makes perfect
a To calculate probability of something, we have to divide the number of favorable outcomes with the number of possible outcomes.
P=Number of favorable outcomes/Number of possible outcomes
Given that a student is an engineering major, the number of possible outcomes (the number of engineering major students) is 920. From the table, we see that 120 of the engineering students live on campus. With this information we can calculate the conditional probability of living on campus given that the student is an engineering major.
P(On campus|Engineering)=120/920≈ 13 %
b The probability of living on campus is the total number of students who live on campus divided by the total number of students.
P(On campus)=12 000/20 000≈ 60 %
The probability of a student living on campus is 60 %, which is higher than the probability of an engineering students living on campus.
c If the events are associated, the probability of living on campus is affected by a student's choice of majoring in engineering. Given the probabilities we calculated in Parts A and B, we see that the probability is much lower if the student is in engineering. Therefore, we can assume the events are associated.
