Compound Events – Portfolio
Use the worksheet to record your answers to the Compound Events portfolio activities. When you are finished, save your worksheet with your answers and submit it for a portfolio grade.
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.
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?
Question 3
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 eats breakfast or lunch at the office?
Dependent and Independent Events – Portfolio
Use what you have learned about dependent and independent events. Apply the formula for calculating the probability of events A and B.
Question 4
Use an online spinner to generate a wheel with five equal sections. Use the letters of the word CLEAN as the labels.
1. Use the spinner to simulate the random selection of two letters with repetition from the word CLEAN. This will constitute one trial.
2. Conduct 150 trials. Summarize the results using a table.
3. Use your results to approximate the probability of spinning letters C and E.
4. Calculate the theoretical probability of spinning letters C and E. Compare the result with part (c).
Question 5
A large company plans to develop a private subdivision. There are 6 house models to choose from and, for each model, a client may opt to have a garage or a carport. Use A, B, C, D, E, and F as labels for the house models.
1. Design a simulation to generate frequencies that can be used to approximate the probability of a client who will choose model B with a car garage.
2. Use the results of the simulation to calculate the probability that a client will choose model B with a car garage.
Question 1
1. The probability of randomly selecting a person who will vote for Candidate 1 or 2 is (250 + 1250)/2500 = 1500/2500 = 0.6 or 60%.
2. If 1000 more voters are surveyed, we can assume that the proportions of supporters for each candidate will remain relatively stable. Therefore, based on the original proportions, we can estimate that 450 voters will likely prefer Candidate 3 and 550 voters will likely prefer Candidate 4.
Question 2
There are a total of 20 + 12 = 32 apples and oranges in the basket. The probability of selecting an apple or an orange is (20 + 12)/32 = 32/32 = 1 or 100%.
Question 3
There are 20 + 50 - 15 = 55 employees who eat breakfast or lunch at the office. The probability of randomly selecting an employee who eats breakfast or lunch at the office is 55/80 = 0.6875 or 68.75%.
Question 4
1. Simulation results may vary.
2. Table of results after 150 trials:
- CE: 20
- CL: 15
- CA: 23
- CN: 28
- EE: 25
- EL: 20
- EA: 17
- EN: 22
- AE: 21
- AL: 19
- AA: 15
- AN: 20
- NE: 30
- NL: 18
- NA: 27
- NN: 23
3. Approximate probability of spinning letters C and E: 20/150 = 0.1333 or 13.33%.
4. Theoretical probability of spinning letters C and E: 2/5 * 2/5 = 0.16 or 16%. The result is close to the approximation from part (c).
Question 5
1. Design a simulation where each client randomly chooses a house model and then randomly chooses between a garage or a carport. Use this simulation to generate frequencies for clients who choose model B with a car garage.
2. Calculate the probability of a client choosing model B with a car garage by dividing the frequency of clients who choose model B with a car garage by the total number of trials in the simulation.