An instructor who taught two sections of engineering statistics last term, the first with 20 students and the second with 30, decided to assign a term project. after all projects had been turned in, the instructor randomly ordered them before grading. consider the first 15 graded projects. (a) what is the probability that exactly 10 of these are from the second section? (round your answer to four decimal places.) (b) what is the probability that at least 10 of these are from the second section? (round your answer to four decimal places.)

(a)

(b)

Step-by-step explanation:

Note that in this problem we have an initial population N = 50, of which 30 fulfill a certain characteristic "m" (belong to the second section). Then, from the population N, a sample of size n = 15 is selected and it is desired to know how many comply with the desired characteristic (second section).

So

Let X be the number of projects in the second section, then X is a discrete random variable that can be modeled by a hypergeometric distribution.

(a)

Therefore, to answer question (a) we use the following equation presented in the attached image:

Where:

Then:

(b)

For part (b) we have:

$12. that is my answer.

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step-by-step explanation: