# A multiple choice test contains 12 questions, each offering 4 possible answers, only 1 of which is correct. A student knows the correct answer to 7 of the questions but randomly guesses the answers to the remaining 5. What is the probability the student will get at least 10 of the 12 correct?

Eric Bizzell | Certified Educator

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Since the student is guaranteed seven correct responses, she needs at least three of the remaining questions to be correct. Thus we need the probability that she gets 3,4, or 5 of the remaining questions correct.

This situation is an example of a binomial probability distribution. Each event can be described in a binary fashion (either correct or incorrect), each event is independent (the results of one does not effect the others), the probabilities do not change, and there are a finite number of events.

The formula for a binomial probability is given by:

`P(x=k)= ._(n)C_(k)(p)^(k)(1-p)^(n-k)`

where k is the number of successes we seek, n is the number of trials, and p is the probability of...

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Rylan Hills | Certified Educator

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