Bot, 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? 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.

Answer 1

Part 1:
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 = (250 + 1,250) / 2,500 = 1,500 / 2,500 = 0.6

Therefore, the probability of randomly selecting a person who will vote for Candidate 1 or 2 is 0.6 or 60%.

Part 2:
If 1,000 more voters are surveyed, we can assume that the distribution of supporters for Candidate 3 and 4 will remain the same. To calculate the number of voters who will likely prefer Candidate 3 or 4, we need to add the number of supporters for Candidate 3 and Candidate 4 in the additional 1,000 voters.

Number of supporters for Candidate 3 = 450
Number of supporters for Candidate 4 = 550

Expected number of supporters for Candidate 3 or 4 in the additional 1,000 voters = (450 + 550) * (1,000 / 2,500) = 1,000

Therefore, if 1,000 more voters are surveyed, it is likely that 1,000 of them will prefer Candidate 3 or 4 based on the previous distribution.

Answer 2

Bot are there any errors in your response?

Answer 3

I apologize for the mistake in my previous response. Let's correct the errors:

Part 1:
The probability of randomly selecting a person who will vote for Candidate 1 or 2 is calculated as follows:
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

Therefore, the correct probability of randomly selecting a person who will vote for Candidate 1 or 2 is 0.6 or 60%.

Part 2:
To determine the number of likely supporters for Candidate 3 or 4 in the additional 1,000 voters, we can calculate it as follows:
Number of supporters for Candidate 3 = 450
Number of supporters for Candidate 4 = 550

Expected number of supporters for Candidate 3 or 4 in the additional 1,000 voters = (Number of supporters for Candidate 3 + Number of supporters for Candidate 4) * (1,000 / (Total number of voters surveyed + 1,000))
Expected number of supporters = (450 + 550) * (1,000 / (2,500 + 1,000))
Expected number of supporters = 1,000 * (1,000 / 3,500)
Expected number of supporters = 285.71

Therefore, if 1,000 more voters are surveyed, it is likely that approximately 285.71 of them will prefer Candidate 3 or 4 based on the previous distribution.