If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. each question has four possible choices. 0.190 0.162 0.085 0.218

There is a 18.97% probability that the student gets exactly four correct.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student gets it correct, or he gets it wrong. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

In this problem we have that:

20 questions, so

Each question has four options and one correct answer, that is guessed, so

Find the probability that the student gets exactly four correct.

This is P(X = 4).

There is a 18.97% probability that the student gets exactly four correct.

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step-by-step explanatio89