Question

Out of 25 students taking a midterm psychology exam, 15 answered the first of two bonus questions, 11 answered the second bonus question, and 1 didn't bother with either one. Round your answer to the nearest percent. What percentage of students tried both questions? What percentage tried at least one question?

Answer 1

Percentage of students who tried both questions =
`8\%`

Percentage of students who tried at least one question =
`96\%`

Explanation:

Given: 25 students take a midterm psychology exam, 15 answered the first of two bonus questions, 11 answered the second bonus question, and 1 didn't bother with either one.

To find: percentage of students who tried both questions and percentage of students who tried at least one question

Solution:

Let A denotes students who answered the first of two bonus questions and B denotes students who answered the second bonus question.

Let U denotes the universal set denoting students who take a midterm psychology exam.

`n(A)=15\,,\,n(B)=11\,,\,n(U)=25`

`n\left ( A'\cap B' \right )=1`

`n\left ( A'\cap B' \right )=n\left ( A\cup B \right )'\\=n(U)-n\left ( A\cup B \right )\\\Rightarrow 1=25-n\left ( A\cup B \right )\\n\left ( A\cup B \right )=25-1=24`

`n\left ( A\cup B \right )=n(A)+n(B)-n\left ( A\cap B \right )\\24=15+11-n\left ( A\cap B \right )\\n\left ( A\cap B \right )=15+11-24=2`

Percentage of students who tried both questions =
`(2)/(25)* 100=8\%`

Percentage of students who tried at least one question =
`(24)/(25)* 100=96\%`