Photo AI
In a survey, 54 people were asked which political party they had voted for in the last three elections - Junior Cycle Mathematics - Question Question - 2013
Question Question
In a survey, 54 people were asked which political party they had voted for in the last three elections. The results are as follows: 30 had voted for the Conservativ... show full transcript
Worked Solution & Example Answer:In a survey, 54 people were asked which political party they had voted for in the last three elections - Junior Cycle Mathematics - Question Question - 2013
Step 1
Represent the information in a Venn diagram.
Answer
To represent the voting data in a Venn diagram, we identify the counts for each intersection:
- Let C represent Conservatives, L represent Liberals, and R represent Republicans.
- The regions of the Venn diagram will be:
- Only Conservatives: 30 - (12 + 8 + 5) = 5
- Only Liberals: 22 - (12 + 9 + 5) = -4 (this indicates overlapping members)
- Only Republicans: 22 - (8 + 9 + 5) = 0
- Conservatives and Liberals (but not Republicans): 12 - 5 = 7
- Liberals and Republicans (but not Conservatives): 9 - 5 = 4
- Conservatives and Republicans (but not Liberals): 8 - 5 = 3
- All three parties: 5
By proper allocation, the counts in the Venn diagram should allow visualization of the overlaps accurately.
Step 2
If one person is chosen at random, what is the probability that the person chosen did not vote in any of the three elections?
Answer
The total number of people surveyed is 54. To find the number of people who did not vote in any party, we consider all who voted:
Total who voted = 54 - (15 + 6 + 10 + 4) = 19
The probability that a person chosen did not vote is:
Step 3
If one person is chosen at random, what is the probability that the person chosen voted for at least two different parties?
Answer
To calculate the probability of someone voting for at least two different parties, we first find the total number of voters who voted for two parties:
- Conservatives and Liberals (not Republicans): 7
- Liberals and Republicans (not Conservatives): 4
- Conservatives and Republicans (not Liberals): 3
- All three parties: 5
Total who voted for at least two parties:
Thus, the probability is:
Step 4
If one person is chosen at random, what is the probability that the person chosen voted for the same party in all three elections?
Answer
To find the probability that a randomly selected person voted for the same party in all three elections, we need to identify those who did so:
Those who voted the same party (all three elections) are counted as: