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An artificial teaching assistant reviews 18 assignments randomly selected from a group of 160. Out of...

An artificial teaching assistant reviews 18 assignments randomly selected from a group of 160. Out of 160 assignments 14 are fraudulent. a. Calculate is the probability that there are no fraudulent homeworks among those reviewed by the algorithm? b. Find the likelihood that there are at least 2 fraudulent homeworks among those reviewed by the algorithm? c. Find the expected number of fraudulent assignments among those reviewed by the algorithm?

Math   Statistics-And-Probability   
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Answer #1

Let X be the random variable denoting the number of fraudulent assignments out of 18 assignments.

The probability of getting a fraudulent assignment = 14/160 = 0.0875

Thus, X ~ Bin(18, 0.0875)

a. The probability that there are no fraudulent homeworks = P(X = 0) = = 0.1924

b. The probability that there are at least 2 fraudulent homework = P(X 2) = = 0.4755

c. The expected number of fraudulent assignments = np = (18 * 0.0875) = 1.575

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