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# Stats Problem Help?

An interviewer is given a list of potential people she can interview. She needs five interviews to complete her assignment. Suppose that each person agrees independently to be interviewed with probability 2/3. What

is the probability she can complete her assignment if the list has 8 names?

I'm stuck on this problem because there is a chance that the interviewer will finish the interviews before getting to 8 names. Anyone know how to solve this?

### 1 Answer

- oldprofLv 72 months agoFavorite Answer
This is a binary distribution problem where p = 1-q and p = 2/3.

p^8 + C7,1 p^7q + C6,2 p^6q^2 + C5,3p^5q^3 are the only success terms as the rest are less than five completions.

When we plug in the numbers we get:

1 0.040606768 < first term

8 0.160002786 < second

28 0.275825699 < third

56 0.271708897 < fourth

0.74814415 <== ANS.

That makes perfect sense, thank you!