Candidate A: 800 votes (32%)
Candidate B: 700 votes (28%)
Candidate C: 600 votes (24%)
Candidate D: 400 votes (16%)
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.
9 answers
Compound Events Portfolio Worksheet
Directions: Use this worksheet to record your answers to the two Compound
Events portfolio activities. When you are finished, save this worksheet with your
answers and submit it for a portfolio grade.
Mutually Inclusive and Exclusive Events -
Portfolio
Record your answers below.
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
a. What is the probability of randomly selecting a person who will vote for
Candidate 1 or 2?
b. If 1,000 more voters are surveyed, how many of them will likely prefer
Candidate 3 or 4? Explain the answer.
Question 2
A basket of fruits contains 20 apples, 4 watermelon slices, and 12 oranges. If
a piece of fruit is to be selected randomly from the box, what is the probability
of selecting an apple or an orange? Explain the process you used.
Directions: Use this worksheet to record your answers to the two Compound
Events portfolio activities. When you are finished, save this worksheet with your
answers and submit it for a portfolio grade.
Mutually Inclusive and Exclusive Events -
Portfolio
Record your answers below.
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
a. What is the probability of randomly selecting a person who will vote for
Candidate 1 or 2?
b. If 1,000 more voters are surveyed, how many of them will likely prefer
Candidate 3 or 4? Explain the answer.
Question 2
A basket of fruits contains 20 apples, 4 watermelon slices, and 12 oranges. If
a piece of fruit is to be selected randomly from the box, what is the probability
of selecting an apple or an orange? Explain the process you used.
a. 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 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 supporters for Candidate 1 and 2: 250 + 1,250 = 1,500
Probability = Number of supporters for Candidate 1 or 2 / Total number of voters surveyed
Probability = 1,500 / 2,500
Probability = 0.6 or 60%
Therefore, the probability of randomly selecting a person who will vote for Candidate 1 or 2 is 0.6 or 60%.
b. If 1,000 more voters are surveyed, the number of voters likely to prefer Candidate 3 or 4 can be calculated based on the percentages from the initial survey:
Percentage of supporters for Candidate 3: 450 / 2,500 = 0.18 or 18%
Percentage of supporters for Candidate 4: 550 / 2,500 = 0.22 or 22%
If 1,000 more voters are surveyed, we can estimate the number of voters likely to prefer Candidate 3 or 4 by applying the percentages to the additional 1,000 voters:
Number of voters likely to prefer Candidate 3: 0.18 * 1,000 = 180
Number of voters likely to prefer Candidate 4: 0.22 * 1,000 = 220
Therefore, if 1,000 more voters are surveyed, 180 of them will likely prefer Candidate 3 and 220 will likely prefer Candidate 4.
Question 2:
To calculate the probability of selecting an apple or an orange from the basket of fruits, we need to add the number of apples and oranges, and divide by the total number of fruits in the basket:
Number of apples: 20
Number of oranges: 12
Total number of apples and oranges: 20 + 12 = 32
Probability = Number of apples or oranges / Total number of fruits in the basket
Probability = 32 / (20 + 4 + 12)
Probability = 32 / 36
Probability = 0.888 or 88.8%
Therefore, the probability of selecting an apple or an orange from the basket of fruits is 0.888 or 88.8%.
Number of supporters for Candidate 1: 250
Number of supporters for Candidate 2: 1,250
Total number of supporters for Candidate 1 and 2: 250 + 1,250 = 1,500
Probability = Number of supporters for Candidate 1 or 2 / Total number of voters surveyed
Probability = 1,500 / 2,500
Probability = 0.6 or 60%
Therefore, the probability of randomly selecting a person who will vote for Candidate 1 or 2 is 0.6 or 60%.
b. If 1,000 more voters are surveyed, the number of voters likely to prefer Candidate 3 or 4 can be calculated based on the percentages from the initial survey:
Percentage of supporters for Candidate 3: 450 / 2,500 = 0.18 or 18%
Percentage of supporters for Candidate 4: 550 / 2,500 = 0.22 or 22%
If 1,000 more voters are surveyed, we can estimate the number of voters likely to prefer Candidate 3 or 4 by applying the percentages to the additional 1,000 voters:
Number of voters likely to prefer Candidate 3: 0.18 * 1,000 = 180
Number of voters likely to prefer Candidate 4: 0.22 * 1,000 = 220
Therefore, if 1,000 more voters are surveyed, 180 of them will likely prefer Candidate 3 and 220 will likely prefer Candidate 4.
Question 2:
To calculate the probability of selecting an apple or an orange from the basket of fruits, we need to add the number of apples and oranges, and divide by the total number of fruits in the basket:
Number of apples: 20
Number of oranges: 12
Total number of apples and oranges: 20 + 12 = 32
Probability = Number of apples or oranges / Total number of fruits in the basket
Probability = 32 / (20 + 4 + 12)
Probability = 32 / 36
Probability = 0.888 or 88.8%
Therefore, the probability of selecting an apple or an orange from the basket of fruits is 0.888 or 88.8%.
A survey of 80 employees was conducted asking about which meals they
regularly eat at the office. Twenty employees eat breakfast at the office, 50
eat lunch, and 15 eat both breakfast and lunch. If an employee is randomly
selected from this group, what is the probability of randomly selecting an
employee who eat breakfast or lunch at the office? Explain how you got the
answer.
d. Calculate the theoretical probability of spinning letters C and E. Compare
the result with part (c).
regularly eat at the office. Twenty employees eat breakfast at the office, 50
eat lunch, and 15 eat both breakfast and lunch. If an employee is randomly
selected from this group, what is the probability of randomly selecting an
employee who eat breakfast or lunch at the office? Explain how you got the
answer.
d. Calculate the theoretical probability of spinning letters C and E. Compare
the result with part (c).
To calculate the probability of randomly selecting an employee who eats breakfast or lunch at the office, we need to consider the following:
- Number of employees who eat breakfast = 20
- Number of employees who eat lunch = 50
- Number of employees who eat both breakfast and lunch = 15
We cannot simply add the number of employees who eat breakfast and lunch because that would count the employees who eat both breakfast and lunch twice. To adjust for this, we need to subtract the number of employees who eat both breakfast and lunch from the total count of employees who eat breakfast and lunch:
Number of employees who eat breakfast or lunch = (Number of employees who eat breakfast) + (Number of employees who eat lunch) - (Number of employees who eat both breakfast and lunch)
Number of employees who eat breakfast or lunch = 20 + 50 - 15 = 55
Probability = Number of employees who eat breakfast or lunch / Total number of employees surveyed
Probability = 55 / 80
Probability = 0.6875 or 68.75%
Therefore, the probability of randomly selecting an employee who eats breakfast or lunch at the office is 0.6875 or 68.75%.
- Calculation for theoretical probability of spinning letters C and E:
If we are spinning a spinner with letters C, D, and E, each letter has an equal chance of being selected. Therefore, the theoretical probability of spinning either C or E is the same, and can be calculated as:
Probability of spinning C or E = Probability of spinning C + Probability of spinning E
Probability of spinning C or E = 1/3 + 1/3 = 2/3
The theoretical probability of spinning letters C or E is 2/3, which is greater than the probability of randomly selecting an employee who eats breakfast or lunch at the office (68.75%). This indicates that the event of spinning C or E has a higher likelihood compared to the event of selecting an employee who eats breakfast or lunch.
- Number of employees who eat breakfast = 20
- Number of employees who eat lunch = 50
- Number of employees who eat both breakfast and lunch = 15
We cannot simply add the number of employees who eat breakfast and lunch because that would count the employees who eat both breakfast and lunch twice. To adjust for this, we need to subtract the number of employees who eat both breakfast and lunch from the total count of employees who eat breakfast and lunch:
Number of employees who eat breakfast or lunch = (Number of employees who eat breakfast) + (Number of employees who eat lunch) - (Number of employees who eat both breakfast and lunch)
Number of employees who eat breakfast or lunch = 20 + 50 - 15 = 55
Probability = Number of employees who eat breakfast or lunch / Total number of employees surveyed
Probability = 55 / 80
Probability = 0.6875 or 68.75%
Therefore, the probability of randomly selecting an employee who eats breakfast or lunch at the office is 0.6875 or 68.75%.
- Calculation for theoretical probability of spinning letters C and E:
If we are spinning a spinner with letters C, D, and E, each letter has an equal chance of being selected. Therefore, the theoretical probability of spinning either C or E is the same, and can be calculated as:
Probability of spinning C or E = Probability of spinning C + Probability of spinning E
Probability of spinning C or E = 1/3 + 1/3 = 2/3
The theoretical probability of spinning letters C or E is 2/3, which is greater than the probability of randomly selecting an employee who eats breakfast or lunch at the office (68.75%). This indicates that the event of spinning C or E has a higher likelihood compared to the event of selecting an employee who eats breakfast or lunch.
A survey of 80 employees was conducted asking about which meals they
regularly eat at the office. Twenty employees eat breakfast at the office, 50
eat lunch, and 15 eat both breakfast and lunch. If an employee is randomly
selected from this group, what is the probability of randomly selecting an
employee who eat breakfast or lunch at the office? Explain how you got the
answer.
regularly eat at the office. Twenty employees eat breakfast at the office, 50
eat lunch, and 15 eat both breakfast and lunch. If an employee is randomly
selected from this group, what is the probability of randomly selecting an
employee who eat breakfast or lunch at the office? Explain how you got the
answer.
To calculate the probability of randomly selecting an employee who eats breakfast or lunch at the office, we use the principle of inclusion-exclusion.
- Number of employees who eat breakfast = 20
- Number of employees who eat lunch = 50
- Number of employees who eat both breakfast and lunch = 15
To find the total number of employees who eat either breakfast or lunch at the office, we need to add the number of employees who eat breakfast and lunch separately and then subtract the number who eat both:
Total employees who eat breakfast or lunch = Employees who eat breakfast + Employees who eat lunch - Employees who eat both breakfast and lunch
Total employees who eat breakfast or lunch = 20 + 50 - 15
Total employees who eat breakfast or lunch = 55
So, out of 80 employees surveyed, there are 55 who eat either breakfast or lunch at the office.
The probability of randomly selecting an employee who eats breakfast or lunch at the office would be:
Probability = Total employees who eat breakfast or lunch / Total number of employees surveyed
Probability = 55 / 80
Probability = 0.6875 or 68.75%
Therefore, the probability of randomly selecting an employee who eats breakfast or lunch at the office is 0.6875 or 68.75%.
- Number of employees who eat breakfast = 20
- Number of employees who eat lunch = 50
- Number of employees who eat both breakfast and lunch = 15
To find the total number of employees who eat either breakfast or lunch at the office, we need to add the number of employees who eat breakfast and lunch separately and then subtract the number who eat both:
Total employees who eat breakfast or lunch = Employees who eat breakfast + Employees who eat lunch - Employees who eat both breakfast and lunch
Total employees who eat breakfast or lunch = 20 + 50 - 15
Total employees who eat breakfast or lunch = 55
So, out of 80 employees surveyed, there are 55 who eat either breakfast or lunch at the office.
The probability of randomly selecting an employee who eats breakfast or lunch at the office would be:
Probability = Total employees who eat breakfast or lunch / Total number of employees surveyed
Probability = 55 / 80
Probability = 0.6875 or 68.75%
Therefore, the probability of randomly selecting an employee who eats breakfast or lunch at the office is 0.6875 or 68.75%.
Use an online spinner to generate a wheel with five equal sections. Use the
letters of the word CLEAN as the labels.
a. Use the spinner to simulate the random selection of two letters with
repetition from the word CLEAN. This will constitute one trial.
b. Conduct 150 trials. Summarize the results using a table.
letters of the word CLEAN as the labels.
a. Use the spinner to simulate the random selection of two letters with
repetition from the word CLEAN. This will constitute one trial.
b. Conduct 150 trials. Summarize the results using a table.
Unfortunately, as a text-based AI, I am unable to create interactive elements like online spinners. However, you can easily find online spinners by searching for "online spinner" on a search engine.
Once you have the spinner with the letters C, L, E, A, and N on the sections, you can simulate the random selection of two letters with repetition from the word CLEAN by spinning the spinner twice for each trial.
To conduct 150 trials:
1. Spin the online spinner twice to select two letters from C, L, E, A, and N.
2. Record the two letters selected for each trial.
3. Repeat this process for a total of 150 trials.
After conducting the 150 trials, summarize the results in a table showing the frequency of each pair of letters selected. This will give you an idea of the likelihood of each pair occurring when randomly selecting two letters with repetition from the word CLEAN.
Once you have the spinner with the letters C, L, E, A, and N on the sections, you can simulate the random selection of two letters with repetition from the word CLEAN by spinning the spinner twice for each trial.
To conduct 150 trials:
1. Spin the online spinner twice to select two letters from C, L, E, A, and N.
2. Record the two letters selected for each trial.
3. Repeat this process for a total of 150 trials.
After conducting the 150 trials, summarize the results in a table showing the frequency of each pair of letters selected. This will give you an idea of the likelihood of each pair occurring when randomly selecting two letters with repetition from the word CLEAN.
1 answer