Use what you have learned about mutually inclusive and exclusive events.
Apply the formula for calculating the probability of events A or B.
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
Candidate 1
Candidate 2
Candidate 3
Candidate 4
Number of Supporters
250
1,250
450
55
Part 1: What is the probability of randomly selecting a person who will vote for Candidate 1 or 2?
(2 points)
• 250/2500
•1500/2500
• 1000/2500
•1250/2250
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. (2 points)
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 then divide by the total number of voters surveyed.
Number of supporters for Candidate 1: 250
Number of supporters for Candidate 2: 1250
Total number of supporters for Candidate 1 or 2: 250 + 1250 = 1500
Total number of voters surveyed: 2500
Probability = Total number of supporters for Candidate 1 or 2 / Total number of voters surveyed
Probability = 1500/2500
Probability = 0.6 or 60%
Part 2:
If 1,000 more voters are surveyed, we can estimate the number of voters who will likely prefer Candidate 3 or 4 by assuming that the proportion of supporters for Candidate 3 or 4 remains the same.
Number of supporters for Candidate 3: 450
Number of supporters for Candidate 4: 55
Total number of supporters for Candidate 3 or 4: 450 + 55 = 505
Assuming the proportion remains the same, for every 2500 voters, 505 will prefer Candidate 3 or 4. Therefore, for 1000 more voters, we can calculate:
505/2500 = X/1000
Cross-multiply: 2500X = 505*1000 = 505000
X = 505000/2500 = 202
Therefore, out of the additional 1000 voters surveyed, approximately 202 of them will likely prefer Candidate 3 or 4.
its 550 not 55
Apologies for the error. Let's correct the calculation with the correct number of supporters for Candidate 4.
Number of supporters for Candidate 4: 550
Total number of supporters for Candidate 3 or 4: 450 + 550 = 1000
Assuming the proportion remains the same, for every 2500 voters, 1000 will prefer Candidate 3 or 4. Therefore, for 1000 more voters, we can calculate:
1000/2500 = X/1000
Cross-multiply: 2500X = 1000*1000 = 1000000
X = 1000000/2500 = 400
Therefore, out of the additional 1000 voters surveyed, approximately 400 of them will likely prefer Candidate 3 or 4.