Question 1 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 a. What is the probability of randomly selecting a person who will vote for Candidate 1 or 2? b. If 1,000 more voters are surveyed, how many of them will likely prefer Candidate 3 or 4? Explain the answer
a. To calculate the probability of randomly selecting a person who will vote for Candidate 1 or 2, we need to add the number of supporters for Candidate 1 and Candidate 2 and divide it by the total number of voters surveyed.
Number of supporters for Candidate 1: 250
Number of supporters for Candidate 2: 1,250
Total number of voters surveyed: 2,500
Probability = (Number of supporters for Candidate 1 + Number of supporters for Candidate 2) / Total number of voters surveyed
Probability = (250 + 1,250) / 2,500
Probability = 1,500 / 2,500
Probability = 0.6 or 60%
Therefore, the probability of randomly selecting a person who will vote for Candidate 1 or 2 is 60%.
b. If 1,000 more voters are surveyed, the likely number of them who will prefer Candidate 3 or 4 can be estimated by assuming that the proportions of supporters for each candidate remain the same.
Number of supporters for Candidate 3: 450
Number of supporters for Candidate 4: 550
Total number of voters surveyed: 2,500
New total number of voters surveyed: 2,500 + 1,000 = 3,500
Proportion of supporters for Candidate 3: 450 / 2,500 = 0.18 or 18%
Proportion of supporters for Candidate 4: 550 / 2,500 = 0.22 or 22%
Number of voters likely to prefer Candidate 3 out of the new survey: 0.18 * 1,000 = 180
Number of voters likely to prefer Candidate 4 out of the new survey: 0.22 * 1,000 = 220
Therefore, if 1,000 more voters are surveyed, it is likely that 180 of them will prefer Candidate 3 and 220 of them will prefer Candidate 4.