An exit poll of 320 voters yielded the following information regarding voting patterns on Propositions A, B, C, and D: 119 voters voted yes on A; 163 voted yes on B; 129 voted yes on C; 142 voted yes on D; 37 voted yes on all four; 25 voted yes on A only; 60 voted yes on B only; 59 voted yes on A and B; 70 voted yes on A and C; 82 voted yes on B and D; 93 voted yes on C and D; 10 voted yes on A, B, and C and no on D; 2 voted yes on A, B, and D and no on C; 16 voted yes on A, C, and D and no on B; and 30 voted yes on B, C, and D and no on A. How many of the surveyed voters voted no on all four propositions?
Question
An exit poll of 320 voters yielded the following information regarding voting patterns on Propositions A, B, C, and D: 119 voters voted yes on A; 163 voted yes on B; 129 voted yes on C; 142 voted yes on D; 37 voted yes on all four; 25 voted yes on A only; 60 voted yes on B only; 59 voted yes on A and B; 70 voted yes on A and C; 82 voted yes on B and D; 93 voted yes on C and D; 10 voted yes on A, B, and C and no on D; 2 voted yes on A, B, and D and no on C; 16 voted yes on A, C, and D and no on B; and 30 voted yes on B, C, and D and no on A. How many of the surveyed voters voted no on all four propositions?
Solution
To find out how many voters voted no on all four propositions, we first need to find out how many voters voted yes on at least one proposition.
From the given data, we have:
- 119 voters voted yes on A
- 163 voters voted yes on B
- 129 voters voted yes on C
- 142 voters voted yes on D
However, these numbers include voters who voted yes on multiple propositions. To avoid double-counting, we need to subtract the number of voters who voted yes on multiple propositions:
- 37 voters voted yes on all four propositions
- 59 voters voted yes on A and B
- 70 voters voted yes on A and C
- 82 voters voted yes on B and D
- 93 voters voted yes on C and D
- 10 voters voted yes on A, B, and C and no on D
- 2 voters voted yes on A, B, and D and no on C
- 16 voters voted yes on A, C, and D and no on B
- 30 voters voted yes on B, C, and D and no on A
Adding these numbers together, we get:
119 + 163 + 129 + 142 - 37 - 59 - 70 - 82 - 93 - 10 - 2 - 16 - 30 = 154
So, 154 voters voted yes on at least one proposition.
Since there were 320 voters in total, the number of voters who voted no on all four propositions is:
320 - 154 = 166
So, 166 of the surveyed voters voted no on all four propositions.
Similar Questions
3/5th of the voters promise to vote for A and the rest promised to vote for B. Of these, on the last day 30% of the voters went back of their promise to vote for A and 25% of voters went back of their promise to vote for B, and A won by 2400 votes. Then, the total number of voters isOptions24000 200001900027500
In a poll for senior class president, 68 of the 145 male students said they planned to vote for Santiago. Out of 139 female students, 89 planned to vote for his opponent, Measha.Construct a conditional relative frequency table based on voter preference. Show your calculations on a separate sheet of paper. Round to the nearest whole percent if necessary.
In a sample of 3,200 registered voters, 1,440, or 45%, approve of the way the President is doing his job. The 45% approval is an example ofGroup of answer choicespopulationsampledescriptive statisticsstatistical inference
On the declaration of election poll dates
The table shows the results of a poll. A total of803 voters selected at random were asked whichcandidate they would vote for in the upcomingelection. According to the poll, if 6,424 people vote inthe election, by how many votes would Angel Cruzbe expected to win?A) 163B) 1,304C) 3,864D) 5,621
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.