SOLUTION: If a student randomly guesses at 20 multiple choice questions, find the probability that the student gets exactly four right. Each answer has four possible choices.

Question 269461: If a student randomly guesses at 20 multiple choice questions, find the probability that the student gets exactly four right. Each answer has four possible choices.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
you want 4 correct and 16 incorrect
there are 20 questions
each question has four answers, so
P(right answer) = 1/4
P(wrong answer) = 3/4
----
Since you want 4 correct of 20 we have a combination of 20C4
This is a binomial problem where p = 1/4, q = 3/4 and we get
(20 "choose" 4)*(probability correct)^(number correct)*(probability incorrect)^(number incorrect)
putting numbers in we get
(20c4)*(1/4)^4*(3/4)^16
This gives us
~ .189685
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