An instructor gives a class a set of 10 problems and says that the nal exam will consist of a random selection of 5 of the problems. If a student has gured out how to solve 7 of the problems, what is the probability that he or she will answer at least 4 problems correctly?

probability that he or she will answer at least 4 problems correctly = 0.5

Step-by-step explanation:

probability that he or she will answer at least 4 problems correctly is given as;

P (at least 4 correctly) = P (exactly 4 correctly) + P (all 5 correctly)

Since there are 10 problems. 4 is from the 7 problems chosen and 1 is from the 3 problems we can't figure out. Thus, P (exactly 4 correctly) = 7C4 x 3C1

Thus, P (at least 4 correctly) = [ (7C4) x (3C1) ] / (10C5) ] + [ (7C5) / (10C5) ]

= [ (35 x3) / 252 ] + [21/252]

= [ 105/252 ] + [ 21/252 ]

= 126 / 252

= 0.5