Part 1: Probability of Selecting a Person Who Will Vote for Candidate 1 or 2
To find the probability of selecting a person who will vote for Candidate 1 or Candidate 2, we first need to determine the total number of supporters for these candidates:
- Supporters for Candidate 1: 250
- Supporters for Candidate 2: 1,250
So, the total number of supporters for Candidates 1 and 2 is:
\[ 250 + 1,250 = 1,500 \]
The total number of surveyed voters is 2,500. Therefore, the probability \( P(A \text{ or } B) \) of selecting a person who will vote for Candidate 1 or Candidate 2 is:
\[ P(A \text{ or } B) = \frac{\text{Number of supporters for Candidates 1 and 2}}{\text{Total number of voters}} = \frac{1,500}{2,500} \]
This simplifies to:
\[ P(A \text{ or } B) = \frac{1,500}{2,500} = \frac{3}{5} \]
Among the given options, the correct response is:
1500 over 2500
Part 2: Preference for Candidate 3 or 4 Among Additional Voters
Now, if 1,000 more voters are surveyed, we must find the new total number of voters and then determine how many of the new participants are likely to prefer Candidates 3 or 4.
Current Supporters:
- Candidate 3: 450 supporters
- Candidate 4: 550 supporters
Total Supporters for Candidates 3 and 4:
\[ 450 + 550 = 1,000 \]
New Total Number of Voters:
\[ 2,500 \text{ (original voters)} + 1,000 \text{ (new voters)} = 3,500 \text{ (total voters)} \]
Assuming the same proportions hold, the percentage of voters who support Candidates 3 and 4 based on the original survey can be calculated:
The proportion of supporters for Candidates 3 and 4 out of the original total is:
\[ \frac{1,000}{2,500} = 0.4 \text{ (or 40%)} \]
Therefore, if we assume the same percentage applies to the new group of 1,000 voters:
\[ \text{Supporters for Candidates 3 and 4 among the new voters} = 1,000 \times 0.4 = 400 \]
Thus, it is likely that 400 out of the 1,000 new voters will prefer Candidates 3 or 4.