On a multiple-choice exam with 3 possible answers for each of the 5 questions, w

Tobias Ali

Tobias Ali

Answered question

2021-10-19

What is the likelihood that a student will get four or more correct answers simply by guessing on a multiple-choice test with three possible answers for each of the five questions?

Answer & Explanation

Velsenw

Velsenw

Skilled2021-10-20Added 91 answers

Define random variable X that marks the number of correct guessed numbers. We have that X{0,1,,5}.
Since every question is guessed independently from every other and there is equal common probability of 1/3 that in every question we would circle the right one, we have that X has Binomial distribution with parameters n=5 and p=1/3. Hence
P(X4)=P(X=4)+P(X=5)=(beg{array}{c}55end{array})(beg{array}{c}13end{array})4(beg{array}{c}23end{array})1+(beg{array}{c}55end{array})(beg{array}{c}13end{array})5(beg{array}{c}23end{array})0
P(X4)=11243
Results:
P(X4)=11243

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