A multiple choice test has 12 questions each of which has 5 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly? A.0.236 B.0.764 C.0.00800 D.0.283

A.0.236

Step-by-step explanation:

For each question, there are only two possible outcomes. Either Judy guesses it correctly, or she does not. The probability of Judy guessing a question correctly 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.

12 questions

This means that

5 possible answers, only one of which is correct.

This means that

If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly?

This is P(X = 3).

So the correct answer is:

A.0.236