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. Probability of selecting a person who will vote for Candidate 1 or 2:
Total number of voters = 2500
Number of voters who will vote for Candidate 1 = 250
Number of voters who will vote for Candidate 2 = 1250
P(Candidate 1 or 2) = P(Candidate 1) + P(Candidate 2)
P(Candidate 1 or 2) = 250/2500 + 1250/2500
P(Candidate 1 or 2) = 1500/2500
P(Candidate 1 or 2) = 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 1000 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 will vote for Candidate 3 = 450
Number of voters who will vote for Candidate 4 = 550
P(Candidate 3 or 4) = P(Candidate 3) + P(Candidate 4)
P(Candidate 3 or 4) = 450/3500 + 550/3500
P(Candidate 3 or 4) = 1000/3500
P(Candidate 3 or 4) = 0.2857
Therefore, out of the additional 1000 voters surveyed, approximately 286 voters will likely prefer Candidate 3 or 4.
Question 2
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) = 0.8889
Therefore, the probability of selecting an apple or an orange from the basket of fruits is 0.8889 or 88.89%.
Question 3
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(eats breakfast or lunch) = P(eats breakfast) + P(eats lunch) - P(eats breakfast and lunch)
P(eats breakfast or lunch) = 20/80 + 50/80 - 15/80
P(eats breakfast or lunch) = 55/80
P(eats breakfast or lunch) = 0.6875
Therefore, the probability of randomly selecting an employee who eats breakfast or lunch at the office is 0.6875 or 68.75%.