A student is taking a multiple-choice exam with 14 questions. Each question has four alternatives. If the student guesses on 10 of the questions, what is the probability she will guess at least 8 correct

0.042% probability she will guess at least 8 correct

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses it correctly, or he does not. The probability of a student 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.

Each question has four alternatives.

One is correct, so

If the student guesses on 10 of the questions, what is the probability she will guess at least 8 correct

This is when . So

0.042% probability she will guess at least 8 correct