MUST SHOW WORK FOR FULL CREDIT
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?
Answer as %.
b. If 1,000 more voters are surveyed, how many of them will likely prefer Candidate 3 or 4? Explain the answer and show work.
a.
Total number of supporters for Candidate 1 and 2 = 250 + 1250 = 1500
Total number of voters surveyed = 2500
Probability of selecting a person who will vote for Candidate 1 or 2 = (Number of supporters for Candidate 1 and 2) / (Total number of voters surveyed)
= 1500 / 2500
= 0.6
= 60%
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, we can assume that the proportions of supporters for each candidate remain the same.
Number of additional voters supporting Candidate 3 or 4 = 1000 * (450 + 550) / 2500
= 1000 * 1000 / 2500
= 400
Thus, if 1,000 more voters are surveyed, approximately 400 of them will likely prefer Candidate 3 or 4.