Mutually Inclusive and Exclusive Events – Portfolio.
Use what you have learned about mutually inclusive and exclusive events. Apply the formula for calculating the probability of events A or B.
Question 1
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
1. What is the probability of randomly selecting a person who will vote for Candidate 1 or 2?
2. If 1,000 more voters are surveyed, how many of them will likely prefer Candidate 3 or 4? Explain your answer.
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.
Total number of supporters for Candidate 1 and Candidate 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 or 60%.
2. If 1,000 more voters are surveyed, the number of supporters for Candidate 3 and 4 can be estimated using the current proportions of supporters.
Since there are 2500 voters surveyed and 1500 of them support Candidate 1 or 2, the remaining 1000 voters are split among Candidate 3 and 4.
Percentage of voters supporting Candidate 3 and 4 = (Number of supporters for Candidate 3 and 4) / (Total number of voters)
Percentage of voters supporting Candidate 3 and 4 = ((2500 - 1500) / 2500) * 100%
Percentage of voters supporting Candidate 3 and 4 = (1000 / 2500) * 100%
Percentage of voters supporting Candidate 3 and 4 = 40%
If 40% of the next 1000 voters surveyed prefer Candidate 3 and 4, then approximately 400 of them will likely prefer Candidate 3 or 4. This estimate is based on the current proportions of supporters and may vary in reality.