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

Answer:

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

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

Step-by-step 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 = $\frac{2}{25}\times 100=8\%$

Percentage of students who tried at least one question = $\frac{24}{25}\times 100=96\%$