Respuesta :
Answer:
5 people trust none of the candidates
Step-by-step explanation:
To know how many people surveyed trust none of the candidates we need to find:
- People that trust all three candidates: 5
- People that just trust candidate B and C: This is equal to people that trust candidate B and C less people that trust all three candidates. So it is equal to: 17 - 5 = 12
- People that just trust candidate A and C: This is equal to people that trust candidate A and C less people that trust all three candidates. So it is equal to: 12 - 5 = 7
- People that just trust candidate A and B: This is equal to people that trust candidate A and B less people that trust all three candidates. So it is equal to: 7 - 5 = 2
- People that just trus candidate C: This is equal to the people that trust candidate C less people that just trust candidate B and C less people that just trust candidate A and C less people that trust all three candidates. So, it is equal to: 48 - 12 - 7 - 5 = 24
- People that just trus candidate B: This is equal to the people that trust candidate B less people that just trust candidate B and C less people that just trust candidate A and B less people that trust all three candidates. So, it is equal to: 44 - 12 - 2 - 5 = 25
- People that just trus candidate A: This is equal to the people that trust candidate A less people that just trust candidate A and C less people that just trust candidate A and B less people that trust all three candidates. So, it is equal to: 34 - 7 - 2 - 5 = 20
Therefore, we can calculate how many people surveyed trust at least one candidate by the sum of the previous quantities as:
5 + 12 + 7 + 2 + 24 + 25 + 20 = 95
Finally, there are 100 people surveyed and 95 people trust at least one candidate, so 5 people trust none of the candidates.
Answer:
5 people trust none of the candidates
Step-by-step explanation:
Given:
n = 100 people
34 people trust candidate A
44 people trust candidate B
48 people trust candidate C
7 people trust candidates both A and B
12 people trust candidates both A and C
17 people trust candidates both B and C
5 people trust candidates all three A and B and C
Number of people that trust only A and B = 7 - 5 = 2
Number of people that trust only A and C = 12 - 5 = 7
Number of people that trust only B and C = 17 - 5 = 12
Number of people that trust only A = 34 - 7 - 5 - 2 = 20
Number of people that trust only B = 44 - 12 - 5 - 2 = 25
Number of people that trust only C = 48 - 7 - 5 - 2 = 24
Number of people that trust at least one candidate
= 20 + 24 + 25 + 7 + 2 + 12 + 5
= 95
The number of people that trust none of the candidates will be:
100 - (20+24+25+7+2+12+5)
= 100 - 95
= 5
5 people trust none of the candidates.
