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? 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.

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? 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 then divide 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 of selecting Candidate 1 or 2 = (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 or 60%

Part 2:

To calculate how many of the additional 1,000 voters will likely prefer Candidate 3 or 4, we first need to find the proportion of voters who prefer Candidate 3 and 4 in the initial survey.

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

Probability of selecting Candidate 3 or 4 = (Number of supporters for Candidate 3 + Number of supporters for Candidate 4) / Total number of voters surveyed
Probability = (450 + 550) / 2,500
Probability = 1,000 / 2,500
Probability = 0.4 or 40%

So, out of the additional 1,000 voters surveyed, we can expect that 40% of them will likely prefer Candidate 3 or 4. This means that 40% of 1,000 will likely prefer Candidate 3 or 4, which is 400 voters.