A mathematics class consists of 17 engineering majors E, 13 science majors S, and 9 liberal arts majors LA. Twelve of the engineering students, 3 of the science majors, and 3 of the liberal arts majors are female. What is the probability that a student selected at random is an engineering major or is a female F?
A)Pr(E∪
F) =
B)Pr(E∪
F) =
C)Pr(E∪
F) =
D)Pr(E∪
F) =
E)Pr(E∪
F) =

Question

A mathematics class consists of 17 engineering majors E, 13 science majors S, and 9 liberal arts majors LA. Twelve of the engineering students, 3 of the science majors, and 3 of the liberal arts majors are female. What is the probability that a student selected at random is an engineering major or is a female F? ​
A)Pr(E∪
F) = 
B)Pr(E∪
F) = 
C)Pr(E∪
F) = 
D)Pr(E∪
F) = 
E)Pr(E∪
F) =

Quizplus · Accepted Answer

There are a total of 17+13+9=39 students in the class. 
The number of female students is 12+3+3=18. 
To find the probability of selecting an engineering major or a female student, we need to add the number of engineering students and female students, but we also need to subtract the number of female engineering students since we counted them twice:

P(E∪F) = (17+18 - 12)/39 = 23/39

Therefore, the best choice is B.

A Mathematics Class Consists of 17 Engineering Majors E, 13