Question

students who take ap english also take the ap exam, of which they either pass or fail. of the 28 students taking ap english, 17 received an a in the course. out of the 16 students that passed the ap exam, 8 received an a. use venn diagram below to organize the information. complete the venn diagram by entering the number of elements in each region and then answer the questions below: region i = region ii = region iii = region iv = how many students failed the ap exam? how many students passed the ap exam and did not receive an a? how many students failed the ap exam and did not receive an a?

Explanation:

Step1: Determine the number of students in the intersection

The number of students who passed the AP - exam and received an A is the intersection of the two sets. Given that 8 students passed the AP - exam and received an A, so Region II = 8.

Step2: Determine the number of students in Region I

The number of students who received an A in the course is 17. Since 8 of them also passed the AP - exam, the number of students who received an A but did not pass the AP - exam (Region I) is \(17 - 8=9\).

Step3: Determine the number of students in Region III

The number of students who passed the AP - exam is 16. Since 8 of them also received an A, the number of students who passed the AP - exam but did not receive an A (Region III) is \(16 - 8 = 8\).

Step4: Determine the number of students in Region IV

The total number of students taking AP English is 28. The number of students in the union of the two sets (\(I + II+III\)) is \(9 + 8+8=25\). So the number of students who neither received an A nor passed the AP - exam (Region IV) is \(28-(9 + 8+8)=3\).

Step5: Determine the number of students who failed the AP - exam

The number of students who failed the AP - exam is the sum of Region I and Region IV, which is \(9 + 3=12\).

Step6: Determine the number of students who passed the AP - exam and did not receive an A

Region III represents the number of students who passed the AP - exam and did not receive an A, which is 8.

Step7: Determine the number of students who failed the AP - exam and did not receive an A

Region IV represents the number of students who failed the AP - exam and did not receive an A, which is 3.

Answer:

Region I = 9
Region II = 8
Region III = 8
Region IV = 3
How many students failed the AP exam? 12
How many students passed the AP exam and did not receive an A? 8
How many students failed the AP exam and did not receive an A? 3