SOLUTION: Set up a table and show all work. A large university employs 43 math professors and 31 English professors. 18 of the math professors teach only night classes, and 22 of the Englis

Question 1141083: Set up a table and show all work.
A large university employs 43 math professors and 31 English professors. 18 of the math professors teach only night classes, and 22 of the English professors teach only day classes. What is the probability that a randomly chosen person from this group is either a math professor or teaches only night classes?
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Probability the chosen professor is a math professor = 43/74 = 0.5811

Probability the chosen professor is a math professor AND teaches only night classes = 18/74 = 0.2432

Probability professor chosen only teaches night classes... This one is tough because they give you the number of math professors that only teach night classes (18), but they do NOT give you the number of English professors that only teach night classes. They DO give you the number of English professors that only teach day classes (22). This means the remaining nine English professors teach night classes. HOWEVER, this does NOT mean nine English professors ONLY teach night classes. Any, all, or none of those nine English professors might teach ONLY night classes. (The key word is ONLY.) So, we simply do not know how many English teachers ONLY teach night classes. This means there is a 1/10 chance for each of the following scenarios:

27 professors teach only night classes (18 math - 9 English)
26 professors teach only night classes (18 math - 8 English)
25 professors teach only night classes (18 math - 7 English)
24 professors teach only night classes (18 math - 6 English)
23 professors teach only night classes (18 math - 5 English)
22 professors teach only night classes (18 math - 4 English)
21 professors teach only night classes (18 math - 3 English)
20 professors teach only night classes (18 math - 2 English)
19 professors teach only night classes (18 math - 1 English)
18 professors teach only night classes (18 math - 0 English)

When you average all these scenarios out...which is the best we can do with the info given to us...22.5 professors teach only night classes. That means the probability the chosen professor teaches only night classes = 22.5/74 = 0.3041

So, the probability the chosen professor is a math professor OR teaches only night classes is as follows:

P(math professor) + P(only night classes) - P(math professor AND only night classes):

0.5811 + 0.3041 - 0.2432 = 0.6420
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