SOLUTION: There are 20 questions on a multiple choice exam, each with four possible answers. If a student guesses on all twenty questions, what is the probability the student gets six questi

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Question 1082467: There are 20 questions on a multiple choice exam, each with four possible answers. If a student guesses on all twenty questions, what is the probability the student gets six questions correct? Express your answer as a percent rounded to the nearest tenth.
A) 16.9%
B) 11.9%
C) 14.9%
D) 18.9%
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
I assume the problem means exactly 6, and not "6 or more":
+%280.25%29%5E6+%2A%280.75%29%5E14+%2A+20C6+=+0.1686+ or 16.9 %
——
+%280.25%29%5E6%2A%280.75%29%5E14+ represents one instance of getting 6 questions correct out of 20 (say the first 6 correct and the remaining 14 incorrect).
20C6 is the number of arrangements of those 6 correct answers out of a field of 20 questions