SOLUTION: Sam sits for a multiple-choice exam with 10 questions, each with 4 possible answers only one which is correct. What is the probability that Sam answers exactly 6 questions correctl

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Question 1149903: Sam sits for a multiple-choice exam with 10 questions, each with 4 possible answers only one which is correct. What is the probability that Sam answers exactly 6 questions correctly by chance alone?
Answer by greenestamps(13216) About Me  (Show Source):
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This is straightforward binomial probability. It applies to a wide range of different kinds of problems. Learn how to use it.

There are 10 questions, we want to choose 6 of them to have correct answers.

The probability of a right answer is 1/4; the probability of a wrong answer is 3/4.

The probability of exactly 6 right answers is then

C%2810%2C6%29%2A%281%2F4%29%5E6%2A%283%2F4%29%5E4

Use a calculator to find that number is about 0.016, or a 1.6% chance.