Community colleges are studying the retention rate of first-year students. It was determined 20 percent of the first-year students don't return. The school contacts 12 students and they all agree to answer a survey given to them by the school.  1) What is the probability that exactly four students do not return after their first year? 2)What is the probability that 1-2 students don not return after the first year? 3) What is the probability that at least five or more students do not return after their first year?

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Community colleges are studying the retention rate of first-year students. It was determined 20 percent of the first-year students don't return. The school contacts 12 students and they all agree to answer a survey given to them by the school. 

1) What is the probability that exactly four students do not return after their first year?

2)What is the probability that 1-2 students don not return after the first year?

3) What is the probability that at least five or more students do not return after their first year? 

Expert Solution
Step 1

Consider,

Probability of success (p) = 20% = 0.20

Number of trials (n) = 12

Consider, X be the random variable that follows the binomial distribution with parameters n = 12 and p = 0.20.

Step 2

(a)

The probability that exactly four students do not return after their first year can be calculated as:

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