The definition of probability of an event is the key to answering this question:
P (A) = the ways that A can occur / Number of total outcomes
Since the student knows how to solve 15 of 20 problems, then there are 5 that the student does not know the answer.
a) In order for 10 correct answers to be chosen on the test means that 0 of the 5 unknown questions NOT be chosen therefore the answer is 1 - 5/20 = 75% or 15/20 = 75%
b)Exactly 8 means that 3/5 unknown would NOT be chosen 1-3/20 = 85%
c) 1-4/20 = 80%