Let F be the event that a student is enrolled in a finance course,and let S be the event that a student is enrolled in a statistics course. It is known that 40% of all students are enrolled in an finance course and 35% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and finance. Find P(S).
A) 0.15
B) 0.35
C) 0.40
D) 0.55
E) 0.60

Question

Quizplus · Accepted Answer

To find P(S), we cannot simply add the percentages of students enrolled in statistics and finance because that would count the students enrolled in both twice. Instead, we can use the formula:
P(S) = P(S or F) - P(S and F)
We are given that P(F) = 0.4, P(S) = 0.35, and P(S and F) = 0.15. 
So, 
P(S) = P(S or F) - P(S and F)
P(S) = P(S) + P(F) - P(S and F) [Using the property P(A or B) = P(A) + P(B) - P(A and B)]
P(S) = 0.35 + 0.4 - 0.15
P(S) = 0.6
Therefore, the answer is B) 0.35.

Let F Be the Event That a Student Is Enrolled