Answer:

?P(A)=number of favorable outcomes to A/Total number of outcomes??

?P(A∪B)=P(A)+P(B)−P(A∩B)?

It is given:

?P(live)=0.45?

?P(not live)=0.55?

?P(meal plan)=0.34?

?P(not meal plan)=0.66?

?P(live∪meal plan)=0.60?

Then;

?P(live∪meal plan)=P(live)+P(meal plan)−P(live∩meal plan)=0.60?

?P(live∪meal plan)=0.45+0.34−P(live∩meal plan)=0.60?

?P(live∩meal plan)=0.19?

A contingency table is shown in the explanation to help you better understand the answers.

1.- What is the probability that a student both lives on campus and has a meal plan?

?P(live∩meal plan)=0.19?

2.- What is the probability that a student neither lives on campus nor has a meal plan?

?P(not live∩not meal plan)=0.40?

3.- What is the probability that a student who does not live on campus has a meal plan?

?P(not live∩ meal plan)=0.15?

4.- Are living on campus and having a meal plan independet?

They are not independent, since the intersection of both events is different than zero. Two events cannot be independent, if both events have a probability of occurring other than zero, as is the case.

5.- If you randomly pick 5 students, what is the probability that at least one of them lives on campus?

?n=5?

?P(live)=0.45?

?P(not live)=0.55?

?P(live)=1−P(not live)?

?P(live≥1)=1−n×P(not live)?

?P(live≥1)=1−0.55×0.55×0.55×0.55×0.55?

?P(live≥1)=1−0.0503?

?P(live≥1)=0.9497?

PFA