An instructor gave her students 12 problems, telling them that 3 of the problems will be on a quiz and that passing the quiz requires solving all 3 of the problems.

a) Given that the instructor chooses the 3 problems at random, what is the probability for a student who knows only 10 problems to pass?

I calculate that the student has 10/12 chances to know the first problem, 9/11 to know the second, and 8/10 to know the third. Therefore the student's probability of passing the quiz is (10/12)*(9/11)*(8/10)= .545

b) What are the chances to fail for a student who knows only 8 problems.

That student has 1 - (8/12)*(7/11)*(6/10) = .745 probability of failing.

Are these answers correct?