If a student answers 40 multiple choice questions, each with four possible answers, by guessing randomly, the probability that she answers at least 15 correctly

Answer 1

prob(right) = 1/4
prob(wrong) = 3/4

prob(at least 15 right)
= prob(15 right) + prob(16 right) + ... + prob(40 right)
or
= 1 - (prob(none right) + prob(1 right) + prob(2 right) + ...+prob(14 right)

I hope you have lots of patience and don't make any errors.

I will do one of the steps for you, after that you are on your own.

prob(12 right)
= C(40,12)(1/4)^12 (3/4)^28
= .1046489

I hope you have a good calculator, on mine I have several memory locations so I can store the individual results and maintain reasonable accuracy

Who would ask such a question?
A textbook?