SOLUTION: A man claims to be able to distinguish between scotch & bourbon 80% of the time. A test of 15 samples is given to him and, if he is correct at least 12 times, he proves his claim.

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Question 260745: A man claims to be able to distinguish between scotch & bourbon 80% of the time. A test of 15 samples is given to him and, if he is correct at least 12 times, he proves his claim. What is the probability his claim is justified, but he does not pass?
Found 2 solutions by richwmiller, drk:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
I believe this was answered over the weekend and they all finished off all the scotch and bourbon and went out for more.

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Lets assume that
P(scotch) = .50
P(bourbon) = .50
We have a binomial distribution here:
P(correct at least 12): (15c12)*(.5^12)(.5^3) +(15c13)*(.5^13)(.5^2) + (15c14)*(.5^14)(.5^1) + (15c15)*(.5^15)(.5^0)
P(correct at least 12) ~ .017578