Question

100 students were asked to ll out a form with three survey questions, as follows: H: Honor Roll

Answer 1

Answer:

1. 45

2. 9

3. 11

4. 17

Step-by-step explanation:

The computation is shown below:

Given  that

28 checked H

26 checked C

14 checked D

8 checked H and C

4 checked H and D

3 checked C and D

2 checked all.

Based on the above information

N(H)=28

N(C) 26

N(D) 14

N(H∪C) = 8

N(H∪D) = 4

$N(C\cup D)=3$

$N(H\cup C\cup D)=2$

We know that

$Total=N(H)+N(C)+N(D)-N(H\cup C)-N(H\cup D)-N(C\cup D)+N(H\cup C\cup D)$

= 28 + 26 + 14 - 8 - 4 - 3 + 2

= 55

1. The students who didnt check any kind of the box is

= 100 - 55

= 45

2) Students who checked exactly two boxes is

$= N(H\cup C)+N(H\cup D)+N(C\cup D)-3N(H\cup C\cup D)$

= 8 + 4 + 3 - 6

= 9

3) Students who checked a minimum of two boxes

$= N(H\cup C)+N(H\cup D)+N(C\cup D)-2N(H\cup C\cup D)$

= 8 + 4 + 3 - 4

= 11

4) Given N(C) = 26

Now we have to deduct N(C∪D) and N(H∪C) as it could be checked aside from the club

= 26 - 8 - 3

= 15

Here the $N(H\cup C\cup D)$ could be deducted twice under both categories so it would be added one time to neutralize

= 15 + 2

= 17

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