An instructor gives his class a set of 15 problems with the

An instructor gives his class a set of 15 problems with the information that the next quiz will consist of a random selection of 4 of them. If a student has figured out how to do 5 of the problems, what is the probability the he or she will answer correctly
(b) at least 3 problems?  

Solution

Number of ways 3 correct answers = 5C3 * 10C1 = 100

Number of ways 4 correct answers = 5C4 * 10C0 = 5

Number of ways getting 4 questions out of 15 = 1365

thus the probability of getting atleast 3 correct answers= (100+5)/1365 = 105/1365 = 0.077