## On a multiple-choice test. Abby randomly guesses on all seven questions. Each question has four choices. Find the probability to the n

Question

On a multiple-choice test. Abby randomly guesses on all seven questions. Each question
has four choices. Find the probability to the nearest thousandth, that Abby gets exactly
three questions correct.

in progress 0
2 weeks 2021-10-01T10:25:09+00:00 1 Answer 0

0.173 probability that she gets exactly three questions correct.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either she guesses the correct answer, or she does not. The probability of guessing the correct answer for 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.

Seven questions:

This means that Each question has four choices.

Abby guesses, which means that Find the probability to the nearest thousandth, that Abby gets exactly three questions correct.

This is P(X = 3).  