Teacher Set Problem Probability

Question

Suppose the professor gives a class a set of 15 problems, with the information that the test will consist of 7 of these. If a student has figured out how to do 12 of the problems, what is the probability he/she will answer correctly:

1. All 7 problems
2. At least 6 problems

Answer 1

about 21%

he can do 12 out of 15, that's 12/15 = 80% chance on each question

.8^7 = about .21 = 21%

expected number of correct answers is .8(7) = 5.6, closer to 6 than 5

for 6 or 7 correct

.8^7 + (.2)(.8^6)(7)) = about .35+.21 = about 56%