THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING:
The number of accidents on a particular highway averages 4.4 per year.Assume that the number of accidents follows a Poisson distribution.
-There are 15 professors in the School of Education.Twelve of them have received good evaluations from students,while 3 received poor evaluations.You will take three courses in the School of Education next semester.What is the probability that all of your professors next semester have received good evaluations?
A)0.516
B)0.484
C)0.258
D)0.242

Question

Quizplus · Accepted Answer

Since there are 15 professors, the probability that one randomly chosen professor received a good evaluation is 12/15 = 0.8. We can assume that the evaluations for each professor are independent of one another.

The probability that all three professors you take next semester have received good evaluations is: 
P(all 3 professors received good evaluations) = P(Good)^3
= (0.8)^3
= 0.512

Therefore, the answer is B) 0.484 as the question is asking for the probability that all professors have received good evaluations, not only at least one professor, so we need to subtract the probability that at least one professor did not receive good evaluations from 1:
P(all professors have received good evaluations) = 1 - P(at least one professor received poor evaluation)
= 1 - [P(1 professor received poor evaluation) + P(2 professors received poor evaluations) + P(3 professors received poor evaluations)]
= 1 - [(Combination of 3 from 15) * (0.8)^2 * (0.2) + (Combination of 2 from 15) * (0.8)^1 * (0.2)^2  + (Combination of 1 from 15) * (0.8)^0 * (0.2)^3]
= 1 - [455 * 0.64 * 0.04 + 105 * 0.8 * 0.04 + 15 * 1 * 0.008]
= 0.484