Question

The students in one college have the following rating system for their professors: excellent, good, fair, and bad. In a recent poll of the students, it was found that they believe that 20% of the professors are excellent, 50% are good, 20% are fair, and 10% are bad. Assume that 12 professors are randomly selected from the college. What is the probability that 4 are excellent and 3 are good?

Answer 1

Answer: Our required probability is 0.0002.

Step-by-step explanation:

Since we have given that

Probability that the professors are excellent = 20% = 0.20

Probability that the professors are good = 50% = 0.50

Probability that the professors are fair = 20% = 0.20

Probability that the professors are bad = 10% = 0.10

Number of professors = 12

We need to find the probability that 4 are excellent and 3 are good.

So, it becomes,

$P(\text{4 are excellent and 3 are good})=(0.2)^4\times (0.5)^3=0.0002$

Hence, our required probability is 0.0002.