Answer:
See below and attached Venn Diagram3
Explanation:
No need to change Venn diagrams It is perfectly clear
- We will represent the different sets of people using letters A and B for convenience
- That total number of people who "Had Drowsiness" is represented by the maroon circle to the left. )Note some of those participants also belong to the category had Nausea)
- We will represent the set of all people who had drowsiness as A and the number of people in that set as n(A) = 95 (given)
- Similarly, the total number of people who had nausea is represented by the aquamarine circle to the right. (Note that some of these people also had drowsiness)
- We will represent the set of all people who had nausea as B and the number of people in that set as n(B) = 77 (given)
- The number of people who had both drowsiness and nausea is the intersection area of the two i.e. the Venn diagram area in the middle which overlaps both the circles. This is represented as A and B and we are given that this number n(A and B) = 58
- This is the number that would go into the center box in the Venn Diagram
- The number of people who had drowsiness but not nausea is the total number of people who had drowsiness - number of people who had both side effects
- This would be n(A) - n(A and B) = 95 - 58 = 37
- This would be the number that would go into the box on the left
- This is referred to as set difference denoted by A - B i.e. the set of all elements in a but not in B. So we say n(A-B) = 37
- Similarly the number of people experiencing nausea but not drowsiness would be set difference B-A and the number of such people would be 77 - 58 = 19
- This number would go into the box on the right
- If we add up all the boxes we get the total number of people who had drowsiness or nausea or both as
- n(A
- or
- ) = 37 + 58 + 19 =
- 114
- You can also arrive at this number by the formula
n(A or B) = n(A) + n(B) - n(A and B)
= 95 + 77 - 58 = 114 - We subtract n(A and B)= 58 because when
we add n(A) and n(B) we are adding this chunk twice so we need to adjust by removing the duplicate addition
- In addition to all these values you will see a box that is outside of any of the circles but inside the circle. This represents the number of people who had no side effects.
- This number would be 161 - 114 = 47
The completed Venn Diagram is attached for your convenience