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.
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 and 2: 250 + 1250 = 1500
Total number of voters surveyed: 2500
Probability = Number of supporters for Candidate 1 and 2 / Total number of voters surveyed
Probability = 1500 / 2500
Probability = 0.6
Therefore, the probability of randomly selecting a person who will vote for Candidate 1 or 2 is 0.6.
Part 2:
If 1,000 more voters are surveyed, we can assume that the distribution of supporters for each candidate remains the same. Therefore, we can expect the same ratio of supporters for Candidate 3 and 4 as we had in the original sample.
Number of supporters for Candidate 3 and 4 in the original sample: 450 + 550 = 1000
If the same ratio is maintained with an additional 1000 voters surveyed, we can expect:
Supporters for Candidate 3: (450/2500) * 1000 = 180
Supporters for Candidate 4: (550/2500) * 1000 = 220
Therefore, 180 voters will likely prefer Candidate 3 and 220 voters will likely prefer Candidate 4 out of the additional 1000 surveyed voters.