There are four presidential candidates in a country. A street survey was conducted asking 2,500 registered voters which candidate they will vote for in the coming election. The table summarizes the results of the survey.
Presidential Candidates Number of Supporters
Candidate 1 250
Candidate 2 1,250
Candidate 3 450
Candidate 4 550
Part 1: What is the probability of randomly selecting a person who will vote for Candidate 1 or 2?
(2 points)
Responses
250/2500
250 over 2500
1500/2500
1500 over 2500
1000/2500
1000 over 2500
1250/2500
1250 over 2500
Question 2
Part 2: If 1,000 more voters are surveyed, how many of them will likely prefer Candidate 3 or 4? Show your work and explain your answer.
Part 1:
To find the probability of randomly selecting a person who will vote for Candidate 1 or 2, we need to add up the number of supporters for Candidate 1 and Candidate 2 and divide it by the total number of registered voters surveyed.
Probability = (Number of supporters for Candidate 1 + Number of supporters for Candidate 2) / Total number of registered voters surveyed
Probability = (250 + 1250) / 2500
Probability = 1500 / 2500
Probability = 0.6 or 60%
Therefore, the probability of randomly selecting a person who will vote for Candidate 1 or 2 is 0.6 or 60%.
Part 2:
If 1,000 more voters are surveyed, we can expect the same distribution of supporters for each candidate as in the initial survey. So, among the additional 1,000 voters, the same proportion of supporters for Candidate 3 and Candidate 4 is likely to be maintained.
From the initial survey, we know that out of 2500 voters, Candidate 3 has 450 supporters and Candidate 4 has 550 supporters. Therefore, to find out how many of the additional 1,000 voters will likely prefer Candidate 3 or 4, we can use the same proportion.
450 supporters out of 2500 voters is:
450/2500 = x/1000
Cross multiply to find x:
2500x = 450 * 1000
2500x = 450000
x = 450000 / 2500
x = 180
Therefore, out of the additional 1,000 voters surveyed, we can expect around 180 to prefer Candidate 3 and 820 to prefer Candidate 4.