A quiz consists of 20 multiple-choice questions, each with 5 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 70 %.

Answer 1

To get 70% or more of 20 questions means that you must get at least 14 of them correct.
prob(correct) = 1/5, prob(not correct) = 4/5

prob(pass)
= C(20,14) (.2)^14 (.8)^6 + C(20,15) (.2)^15 (.8)^5 + ...
... + C(20,20)(.2)^20 (.8)^0
= .000001664 + .000000166 + ..... + 1.0486(10^-14)
= appr .00000183

since the terms get rapidly smaller, I only added the first two terms
(my calculator kicked into scientific notation of the answer after the 3rd term)