Question

A student is taking a multiple-choice exam with 16 questions. Each question has five alternatives. If the student guesses on 12 of the questions, what is the probability she will guess at least 8 correct? Assume all of the alternatives are equally likely for each question on which the student guesses.

I thought this was pretty easy but I cannot figure it out!

Answer 1

You need to add the probabilities of getting 8,9,10,11,12,13,14,15 and 16 right

The probability of getting 8 right (and 8 wrong) is
(0.2)^8*(0.8)^8*[16!/(8!*8!)]= 0.00553

The probability of getting 9 right (and 7 wrong) is
(0.2)^9*(0.8)^7*[16!/(7!*9!)]= 0.00122

etc. The probability of getting higher numbers right drops off very fast

The probability of getting 16 right is (0.2)^16 = 7*10^-12 (i.e negligible)

Answer 2

.0069