Question

An exam consists of 16 ​multiple-choice questions. Each of the 16 answers is either right or wrong. Suppose the probability that a student makes fewer than 5 mistakes on the exam is 0.47 and that the probability that a student makes from 5 to 7 ​(inclusive) mistakes is 0.14. Find the probability of each of the following outcomes.

A student makes more than 7 mistakes

Answer 1

the probability that a student makes more than 7 mistakes on the exam is 0.39.

Explanation:

Let X be the number of mistakes a student makes on the exam. Then, X follows a binomial distribution with n=16 and some unknown probability of success p (i.e., the probability of answering a question correctly).

We know that P(X<5) = 0.47 and P(5<=X<=7) = 0.14. Using the complement rule, we can find P(X>7) as follows:

P(X>7) = 1 - P(X<=7)

= 1 - P(X<5) - P(5<=X<=7)

= 1 - 0.47 - 0.14

= 0.39

Therefore, the probability that a student makes more than 7 mistakes on the exam is 0.39.