a. To calculate the probability of randomly selecting a person who will vote for Candidate 1 or Candidate 2, we need to add up the number of supporters for both candidates and divide by the total number of voters surveyed.
Total number of supporters for Candidate 1 and Candidate 2 = 250 (Candidate 1) + 1250 (Candidate 2) = 1500
Total number of voters surveyed = 2500
Probability = Total number of supporters for Candidate 1 and 2 / Total number of voters surveyed
Probability = 1500 / 2500
Probability = 0.6
To convert this to a percentage, we multiply by 100:
Probability = 0.6 * 100 = 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, we can use the same probability calculated above to estimate how many of the additional voters will prefer Candidate 3 or Candidate 4.
Total number of voters after surveying additional 1,000 voters = 2500 + 1000 = 3500
To estimate the number of voters who will prefer Candidate 3 or Candidate 4, we use the probability of 0.6 calculated in part a.
Estimated number of voters who prefer Candidate 3 or Candidate 4 = Probability * Total number of voters after surveying 1,000 voters
Estimated number of voters who prefer Candidate 3 or Candidate 4 = 0.6 * 3500
Estimated number of voters who prefer Candidate 3 or Candidate 4 = 2100
Therefore, if 1,000 more voters are surveyed, it is likely that approximately 2,100 of them will prefer Candidate 3 or Candidate 4.
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.
1 answer