Question

) An instructor gives his class a set of 18 problems with the information that the next quiz will consist of a random selection of 9 of them. If a student has figured out how to do 13 of the problems, what is the probability the he or she will answer correctly

Answer 1

The probability the he or she will answer correctly is 1.5%

Explanation:

In all, there are 18 problems. In this question, the order of which the problems are sorted for the quiz makes no difference. For example, if the question A of the quiz is P1 and question B P2, and question A P2 and question B P1, it is the same thing.

There are 18 problems and 9 are going to be selected. So, there is going to be a combination of 9 elements from a set of 18 elements.

A combination of n elements from a set of m objects has the following formula:

`C_((m,n)) = (m!)/(n!(m-n)!)`

In this question, m = 18, n = 9. So the total number of possibilities is:

`T_(p) = C_((18,9)) = (18!)/(9!(18-9)!) = 48620`

Now we have to calculate the number of desired outcomes. This number is a combination of 9 elements from a set of 13 elements(13 is the number of problems that the student has figured out how to do).

Now, m = 13, n = 9. The number of desired possibilities is:

`D_(p) = C_((13,9)) = (13!)/(9!(13-9)!) = 715`

The probability is the number of desired possibilities divided by the number of total possibilities. So

`P = (715)/(48620) = 0.015 = 1.5%`

The probability the he or she will answer correctly is 1.5%