In a certain city, the population of voters is 4000 . The pattern of voting remains approximately the same each election, though individuals may change their party. Of those listed a Democrat 82% will vote Democratic in the next election, 10% will vote Republican in the next election and the rest will vote for a third party candidate. Of those voting Republican in the last election 15% will vote Democratic in the next election, 5% will vote for a third party and the rest will remain voting for Republicans. Of those who voted for a third party candidate last time 30% will vote for a Republican next time, 40% will vote Democratic and the rest will again vote for the third party candidate.
Let's break down the given information:
Population of voters = 4000
Percentage of Democrats voting Democratic in the next election = 82%
Percentage of Democrats voting Republican in the next election = 10%
Percentage of Democrats voting for a third party candidate in the next election = 8% (100% - 82% - 10%)
Percentage of Republicans voting Democratic in the next election = 15%
Percentage of Republicans voting for a third party candidate in the next election = 5%
Percentage of Republicans remaining voting for Republicans = 100% - 15% - 5% = 80%
Percentage of third-party voters voting Republican in the next election = 30%
Percentage of third-party voters voting Democratic in the next election = 40%
Percentage of third-party voters remaining voting third-party = 100% - 30% - 40% = 30%
Let's calculate the number of voters in each category for the next election:
Number of Democratic voters = 4000 * 82% = 3280
Number of Republican voters = 4000 * 10% + 4000 * 15% = 400 + 600 = 1000
Number of third-party voters = 4000 * 8% + 4000 * 5% + 4000 * 40% = 320 + 200 + 1600 = 2120
Therefore, the approximate number of voters in each category for the next election will be as follows:
- Democratic voters: 3280
- Republican voters: 1000
- Third-party voters: 2120
To determine the expected number of voters for each party in the next election, we can follow these steps:
Step 1: Calculate the number of voters who will vote Democratic in the next election.
- 82% of the Democrats from the last election will vote Democratic again: 0.82 * 4000 = 3280 voters.
- 15% of the Republicans from the last election will switch and vote Democratic: 0.15 * 4000 * 0.10 = 60 voters.
- 40% of the third-party voters from the last election will switch and vote Democratic: 0.40 * 4000 * (1 - 0.82 - 0.15) = 204 voters.
Total Democratic voters = 3280 + 60 + 204 = 3544 voters.
Step 2: Calculate the number of voters who will vote Republican in the next election.
- 10% of the Democrats from the last election will switch and vote Republican: 0.10 * 4000 * 0.82 = 328 voters.
- The remaining Republicans from the last election will stay with the party: 4000 * 0.10 = 400 voters.
- 30% of the third-party voters from the last election will switch and vote Republican: 0.30 * 4000 * (1 - 0.82 - 0.15) = 384 voters.
Total Republican voters = 328 + 400 + 384 = 1112 voters.
Step 3: Calculate the number of voters who will choose a third party in the next election.
- The remaining voters who didn't choose the Democratic or Republican parties: 4000 - 3544 - 1112 = 344 voters.
So, the expected number of voters for each party in the next election are as follows:
- Democratic: 3544 voters
- Republican: 1112 voters
- Third party: 344 voters.