This question has two parts: 2. Suppose 1 in 5 college interns turns out to be a

Question

This question has two parts:
2. Suppose 1 in 5 college interns turns out to be a great employee.

2.1 How many interns would you need to try out to have a 90% chance of finding at least one great employee? Using the binomial, write the equation defining the solution then solve for n.

2.2 How many interns would you need to try out to have a 90% chance of finding two or more great employees? This turns out to be hard to solve explicitly, but it is still easy to write the simple equation defining the solution implicitly using the binomial. So, work it out up to the point where it is ugly to solve. You can use trial and error or a numerical solution technique to get the actual answer if you want, but that is not required. We will do that later with software.

Explanation / Answer

p = 1/5 = 0.2

2.1) P(X > 1) = 1 - P(X = 0) = 1 - nC0 * 0.20 * 0.8n

So, 0.9 = 1 - 0.8n

or, 0.8n = 0.1

or, n ln(0.8) = ln(0.1)

or, n = ln(0.1) / ln(0.8)

or, n = 10.3 or 10(approx)

2.2) P(X > 2) = 1 - [P(X = 0) + P(X = 1)] = 1 - [nC0 * 0.20 * 0.8n + nC1 * 0.21 * 0.8n-1]

or, 0.9 = 1 - [0.8n + 0.2n * 0.8n-1]

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