Question

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 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

2502500
250 over 2500

15002500
1500 over 2500

10002500
1000 over 2500

12502500
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.(2 points)

Answer 1

[AI-generated answer — Bot GPT 3.5]

Part 1:

To calculate the probability of randomly selecting a person who will vote for Candidate 1 or 2, we add the number of supporters for Candidate 1 and Candidate 2 and divide by the 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 60%.

Part 2:
If 1,000 more voters are surveyed, we can assume that the proportions of supporters for each candidate remain the same. We can calculate the number of voters who will likely prefer Candidate 3 or 4 by adding the number of supporters for Candidate 3 and Candidate 4 and then dividing by the total number of voters.

Number of voters supporting Candidate 3 or 4 = (450 + 550) / (2500 + 1000)
Number of voters supporting Candidate 3 or 4 = 1000 / 3500
Number of voters supporting Candidate 3 or 4 = 0.2857 or 28.57%

Therefore, if 1,000 more voters are surveyed, it is likely that 28.57% of them will prefer Candidate 3 or 4.