really confused on this problem?

Question

A main claims to be able to distinguish between scotch and 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 doesnt pass the test?

Answer 1

Drag out your binomial formula.

15 trials. .8 probability of success per trial. The question is to find the probability of no more than 11 successes.

It's actually easier to turn it around, saying there's a 20% chance of failure, and ask what the probability is of at least 4 failures in 15 tries.

Answer 2

72%.... Real easy, actually