SOLUTION: A student takes a 4-question, multiple-choice quiz with 3 choices for each question. If the student guesses on each question, what is probability that student guesses exactly 1 que
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Question 1011356: A student takes a 4-question, multiple-choice quiz with 3 choices for each question. If the student guesses on each question, what is probability that student guesses exactly 1 question correct?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
A student takes a 4-question, multiple-choice quiz with 3 choices for each question. If the student guesses on each question, what is probability that student guesses exactly 1 question correct?
Solution:
The problem can be solved using the binomial distribution, with
probability of success, p = 1/3 (a constant throughout the experiment)
number of trials, n = 4
We need to assume that the answers are random and independent.
The required probability is for x = 1 = number of correct answers (out of 4).
where
and
C(n,x)=number of combinations for n choose x = n!/(x!(n-x)!)
Substituting values,
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