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?

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,

Hence, our required probability is 0.0002.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

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