A sample poll of 100 voters revealed the following information concerning three candidates A, B, and C who were running for three offices. 10 voted in favor of both A and B, 35 voted in favor of A or B but not C, 25 voted in favor of B but not A or C, 65 voted in favor of B or C but not A, 25 voted in favor of C but not A or B, 0 voted in favor of A and C but not B. How man voters did not favor any of the candidates
Well, based on the information you've given me, it seems like there's quite a bit of confusion among the voters! It's like they're competing in their own little comedy sketch!
Let's break it down. We have three candidates, A, B, and C, running for three offices. Now, I'm assuming these voters aren't auditioning for a three-ring circus, but who knows?
Here's what we know from the Poll:
- 10 voters are in favor of both A and B. These folks must be having trouble making up their mind. It's like trying to decide between chocolate cake and ice cream—can't blame them!
- 35 voters lean towards A or B, but not C. Well, looks like these voters can't handle the three-ring circus and are all about the main acts. Who needs the clowns, right?
- 25 voters are fans of only B, but don't care for A or C. Ah, the B lovers. They must find B simply irresistible. Maybe B knows some great magic tricks!
- 65 voters enjoy either B or C, but not A. These folks must be looking for some action, but not the kind that candidate A is offering. Maybe they're fans of acrobatics or fire-breathing?
- 25 voters are into C, but not A or B. These folks are giving all their attention to candidate C. Maybe C is a ventriloquist, and the voters are mesmerized by the puppetry!
Now, let's find out how many voters didn't favor any of the candidates. To do that, we need to analyze the last information you provided.
- Apparently, no one voted for A and C without picking B. Well, if there was an act that combined candidate A's political rhetoric with candidate C's juggling skills, maybe they'd have a chance!
Okay, jokes aside, let's calculate the number of voters who didn't favor any of the candidates:
To do this, we need to add up the number of voters who favor each candidate separately:
Voters favoring A: 10 (both A and B) + 35 (only A or B, not C) + 0 (A and C, not B) = 45 voters favoring A.
Voters favoring B: 10 (both A and B) + 35 (only A or B, not C) + 25 (only B, not A or C) + 65 (B or C, not A) = 135 voters favoring B.
Voters favoring C: 65 (B or C, not A) + 25 (only C, not A or B) = 90 voters favoring C.
Now, let's add up the total number of voters who favor any candidate:
45 (voters favoring A) + 135 (voters favoring B) + 90 (voters favoring C) = 270 voters favoring at least one candidate.
Since the poll sampled 100 voters, we can subtract the number of voters favoring any candidate from the total to find the number of voters not favoring any candidate:
100 (total voters) - 270 (voters favoring at least one candidate) = -170
Uh-oh! It seems like I've misplaced my clown calculator, and the final number came out as a negative! That's definitely not right!
So, to answer your question, it appears that there may have been an error in the provided data. Unfortunately, I don't have the correct answer for you at the moment. But hey, at least I provided you with a little laughter along the way, right?
To find the number of voters who did not favor any of the candidates, we need to calculate the number of voters who do not fall into any of the given categories.
Let's break down the given information into different groups:
- 10 voted in favor of both A and B.
- 35 voted in favor of A or B but not C.
- 25 voted in favor of B but not A or C.
- 65 voted in favor of B or C but not A.
- 25 voted in favor of C but not A or B.
- 0 voted in favor of A and C but not B.
Now let's create a Venn diagram to help us visualize the relationships between the groups:
```
A C
/ \ / \
/ \ / \
/ 10 \ / 25 \
B/---------\ /---------\
\ 35 / \ 65 /
\ / \ /
\ / \ /
X Y
```
Let X represent the number of voters who voted in favor of A and C, and let Y represent the number of voters who did not favor any of the candidates.
From the diagram, we can see that:
- The number of voters who voted in favor of A is 10 (A + X + 35).
- The number of voters who voted in favor of B is 10 (B + X + 25 + Y).
We also know that:
- The total number of voters who voted in favor of A, B, or C is 100.
- The number of voters who voted in favor of B or C but not A is 65 (65 + X).
Using this information, we can set up the following equations:
A + B + C + X + Y = 100 (1)
A + X + 35 = 10 (2)
B + X + 25 + Y = 10 (3)
B + C + X + 25 + Y = 65 (4)
Simplifying equations (2), (3), and (4), we get:
A + X = -25 (5)
B + X + Y = -15 (6)
C + X + Y = 40 (7)
Now, let's solve these equations to find the values of A, B, C, X, and Y:
From equation (5), we can see that A + X = -25. Since the number of voters could not be negative, we know that A + X = 0.
Substituting this into equation (7), we have:
0 + Y = 40
Y = 40
So, the number of voters who did not favor any of the candidates is 40.
To find the number of voters who did not favor any of the candidates, we need to subtract the total number of voters who favored at least one candidate from the total number of voters in the sample.
Let's break down the information given in the poll and calculate the number of voters who favored at least one candidate:
10 voted in favor of both A and B.
25 voted in favor of B but not A or C.
25 voted in favor of C but not A or B.
To find the number of voters who favored at least one candidate, we add these three numbers together:
10 + 25 + 25 = 60
Therefore, 60 voters favored at least one of the candidates.
Now, we can find the number of voters who did not favor any candidate:
Total number of voters - Number of voters who favored at least one candidate = Number of voters who did not favor any candidate
In this case, the total number of voters in the sample is given as 100.
100 - 60 = 40
So, there were 40 voters who did not favor any of the candidates.