A multiple-choice test has 27 questions. Each question has 5 possible answers, of which only one is correct. What is the probability that sheer guesswork will yield exactly 18 correct answers?

Around 0% probability that sheer guesswork will yield exactly 18 correct answers

Step-by-step explanation:

For each question, there are only two possible outcomes. Either you guess the correct answer, or you do not. The probability of guessing the correct answer is a question is independent of other questions. So we use the binomial probability distribution to solve this question.

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 combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

A multiple-choice test has 27 questions.

This means that

Each question has 5 possible answers, of which only one is correct.

This means that

What is the probability that sheer guesswork will yield exactly 18 correct answers?

This is P(X = 18).

Around 0% probability that sheer guesswork will yield exactly 18 correct answers

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step-by-step explanation: