Among 500 freshmen pursuing a business degree at a universit

Among 500 freshmen pursuing a business degree at a university, 306 are enrolled in an economics course, 237 are enrolled in a mathematics course, and 138 are enrolled in both an economics and a mathematics course. What is the probability that a freshman selected at random from this group is enrolled in each of the following? (Enter your answers to three decimal places.) (a) an economics and/or a mathematics course (b) exactly one of these two courses (c) neither an economics course nor a mathematics course

Solution

P(A)=306/500. Let\'s say the event A is a student enrolled in an economics course.

P(B)= P(B)=237/500. Now event B is a student enrolled in a mathematics course

Now P(AB)=138/500 is for students enrolled in both

(a) P(AUB) is the probability a student is enrolled in economics or mathematics

So, P(AUB)=P(A)+P(B)-P(AB)=(306+237-138)/500=405/500=0.81

(b) P(AB\') is the probability that someone is taking economics but not math. P(A\'B) is probability someone is taking math but not economics

P(AB\')=P(A)-P(AB)=(306-138)/500=168/500=0.33
P(A\'B)=P(B)-P(AB)=(237-138)/500=99/500=0.19
Now if we add these two cases together:

P(AB\')+P(A\'B)=(168+99)/500=306/500=0.53

(c)  P(U)-P(AUB), or (500-405)/500=95/500.=0.19