A multiple choice test has ten questions each with four possible answers of which only one is the correct answer. what is the probability that sheer guess work yields 5 to 10 correct answers?

This can be solved by using the binomial distribution, where the probability of guessing the correct answer to a question is 0.25.

P (5 correct) = 0.0584

P (6 correct) = 0.0162

P (7 correct) = 0.0031

P (8 correct) = 0.0004

P (9 correct) = 0.0000

P (10 correct) = 0.0000

P (5 to 10 correct) = 0.0781 or 7.81%