Stats Problem Help?

Question

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?

oldprof · Accepted 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.

Stats Problem Help?

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