An instructor gives his class a set of 20 problems with the information that the next quiz will consist of a random selection of 10 of them. if a student has figured out how to do 16 of the problems, what is the probability the he or she will answer correctly
(a) all 10 problems?
(b) at least 9 problems?

(a) Probability he or she will answer all 10 problems correctly is 0.5

(b) Probability he or she will answer at least 9 problems correctly is 0.95

Step-by-step explanation:

(a) Probability is given by number of possible outcomes ÷ number of total outcomes

Number of possible outcomes = 10 problems

Number of total outcomes = 20 problems

Probability he or she will get all 10 problems correctly = 10 ÷ 20 = 0.5

(b) Probability he or she gets at least 9 problems correctly means he or she either gets 9 or the 10 problems correctly

Probability he or she gets at least 9 problems correctly = (9÷ 20) + (10÷20) = 0.45+0.5 = 0.95