SOLUTION: A Multiple-choice test has 15 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question.
a. What is the
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-> SOLUTION: A Multiple-choice test has 15 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question.
a. What is the
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Question 320257: A Multiple-choice test has 15 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question.
a. What is the probability of getting exactly 5 correct answers?
b. What is the probability of getting less than 6 correct answers?
Part a. You want the probability of successes out of trials where the probability of success on any given trial is .
where is the number of combinations of things taken at a time and is computed by .
For this particular problem:
and
Hence you need to calculate:
where is the number of combinations of things taken at a time and is computed by .
I'll leave the calculator work to you.
Part b. The probability of getting less than 6 correct is the sum of the probability of getting exactly 0 plus exactly 1 plus...plus exactly 5. In other words:
