There are 1000 Psychology majors at PSY U there are 200 psyc

There are 1,000 Psychology majors at PSY U., there are 200 psychology students enrolled in an introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory to psychology course.  There are an additional 250 psychology students enrolled in introduction to psychology but not enrolled in statistics.  If a psychology student is selected at random, what is the probability that the student is either enrolled in introduction to psychology or statistics, but not both?

A) 0.45
B) 0.50
C) 0.40
D) 0.05
E) None of the above

Solution

Let P shows the event student enroll only for introduction to psychology and S shows the event that student enroll only for introductory statistics course. Since out of 200 students who enrolled for introductory statistics course, 50 also enrolled for introductory to psychology course. So the number of student , enrolled only for introductory statistics course is 200-50 -150. Therefore

P(S)=150/1000=0.15

P(P)=250/1000=0.25

Therefore, the probability that the student is either enrolled in introduction to psychology or statistics, but not both is

P(S or P)=P(S)+P(P)=0.15+0.25=0.40

Hence, option (c) is correct.