Question

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
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? 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.

Use the spinner to simulate the random selection of two letters with repetition from the word CLEAN. This will constitute one trial.
Conduct 150 trials. Summarize the results using a table.
Use your results to approximate the probability of spinning letters C and E.
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.

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.
Use the results of the simulation to calculate the probability that a client will choose model B with a car garage.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Question 1

Probability of selecting a person who will vote for Candidate 1 or 2:
Total number of voters = 2500
Number of voters who support Candidate 1 = 250
Number of voters who support Candidate 2 = 1250

P(Candidate 1 or 2) = P(Candidate 1) + P(Candidate 2) - P(Candidate 1 and 2)
P(Candidate 1 or 2) = 250/2500 + 1250/2500 - 0
P(Candidate 1 or 2) = 1500/2500
P(Candidate 1 or 2) = 0.6

If 1,000 more voters are surveyed, the number of voters who will likely prefer Candidate 3 or 4 can be calculated as follows:
Number of voters who support Candidate 3 = 450
Number of voters who support Candidate 4 = 550

P(Candidate 3 or 4) = P(Candidate 3) + P(Candidate 4) - P(Candidate 3 and 4)
P(Candidate 3 or 4) = 450/3500 + 550/3500 - 0
P(Candidate 3 or 4) = 1000/3500
P(Candidate 3 or 4) ≈ 0.2857

Question 2

Probability of selecting an apple or an orange:
Total number of fruits = 20 + 4 + 12 = 36
Number of apples = 20
Number of oranges = 12

P(apple or orange) = P(apple) + P(orange)
P(apple or orange) = 20/36 + 12/36
P(apple or orange) = 32/36
P(apple or orange) = 8/9

Question 3

Probability of selecting an employee who eats breakfast or lunch:
Total number of employees = 80
Number of employees who eat breakfast = 20
Number of employees who eat lunch = 50
Number of employees who eat both breakfast and lunch = 15

P(breakfast or lunch) = P(breakfast) + P(lunch) - P(breakfast and lunch)
P(breakfast or lunch) = 20/80 + 50/80 - 15/80
P(breakfast or lunch) = 55/80
P(breakfast or lunch) = 0.6875

Question 4

Results of 150 trials of spinning letters C and E:

| C and E | Frequency |
|----------|----------|
| Yes | 21 |
| No | 129 |

Probability of spinning letters C and E ≈ 21/150 ≈ 0.14

Theoretical probability of spinning letters C and E:
P(C) = 1/5
P(E) = 1/5
P(C and E) = P(C) * P(E) = 1/5 * 1/5 = 1/25 = 0.04

The experimental probability in part (c) is higher than the theoretical probability in part (d).

Question 5

Simulation for client choosing model B with a car garage:

| Model B with car garage | Frequency |
|---------------------------|----------|
| Yes | 25 |
| No | 125 |

Probability of a client choosing model B with a car garage ≈ 25/150 ≈ 0.1667

Answer 2

make it like a 7 grader did it

Answer 3

[AI-generated answer — Bot GPT 3.5]

Question 1

What is the chance of picking someone who supports Candidate 1 or 2?
Total voters = 2500
Support for Candidate 1 = 250
Support for Candidate 2 = 1250

P(Candidate 1 or 2) = P(Candidate 1) + P(Candidate 2) - P(Candidate 1 and 2)
P(Candidate 1 or 2) = 250/2500 + 1250/2500 = 1500/2500 = 0.6

If 1000 more voters are surveyed, how many will likely prefer Candidate 3 or 4?
Support for Candidate 3 = 450
Support for Candidate 4 = 550

P(Candidate 3 or 4) = 450/3500 + 550/3500 = 1000/3500 ≈ 0.2857

Question 2

What is the possibility of selecting an apple or an orange?
Total fruits = 20 + 4 + 12 = 36
Number of apples = 20
Number of oranges = 12

P(apple or orange) = 20/36 + 12/36 = 32/36 = 8/9

Question 3

What is the likelihood of choosing an employee who eats breakfast or lunch?
Total employees = 80
Employees who eat breakfast = 20
Employees who eat lunch = 50
Employees who eat both = 15

P(breakfast or lunch) = 20/80 + 50/80 - 15/80 = 55/80 ≈ 0.6875

Question 4

Results after spinning the letters C and E 150 times:

| C and E | Frequency |
|----------|----------|
| Yes | 21 |
| No | 129 |

Probability of spinning letters C and E ≈ 21/150 ≈ 0.14

Theoretical probability of spinning letters C and E:
P(C) = 1/5
P(E) = 1/5
P(C and E) = P(C) * P(E) = 1/25 = 0.04

The actual probability is higher than the theoretical probability.

Question 5

Simulation for clients choosing model B with a car garage:

| Model B with car garage | Frequency |
|---------------------------|----------|
| Yes | 25 |
| No | 125 |

Probability ≈ 25/150 ≈ 0.1667