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Unit 3 Tutorial
Exercise Set 3A Calculating Probabilities
Solutions can be found on page 6
1. Over a long period of time, the queue length of customers at the teller section of a major bank was observed to have the following probability distribution;
Number in queue
Probability
0
0.1
1
0.2
2
0.2
3
0.3
4 or more
0.2
Find the probability of
a. At most two people in the queue.
b. No more than three people in the queue.
c. At least one person in the queue.
d. Two or more people in the queue.
e. Given there is at least one person in the queue, what is the probability that there are 4 or more?
2. An airline has offered a special vacation package to Fiji. The length of stay is either for 3 days or 7 days, and the type of accommodation can be either economy, regular, or deluxe.
Consider the experiment of observing the choices made by the next person signing up for the package.
i.
How many experimental outcomes are possible?
ii. Draw a tree diagram for this experiment.
3. An investor has two stocks: stock A and stock B. Each stock may increase in value, decrease in value, or remain unchanged. Consider the experiment as the investment in both of the two stocks.
i.
How many experimental outcomes are possible?
ii. Draw a tree diagram for the experiment. iii. How many of the experimental outcomes result in an increase in value for at least one of the two stocks? iv. How many of the experimental outcomes result in an increase in value for both of the stocks?
4. Suppose that a manager of a large apartment complex provides the following subjective probability estimates about the number of vacancies that will exist next month:
Vacancies
0
1
2
3
4
5
Probability
.05
.15
.35
.25
.10
.10
List the components of each of the following events and calculate the probability of the events:
(a) No vacancies.
(b) At least four vacancies.
(c) Two or fewer vacancies.
5. The manager of a furniture store
Exercise Set 3A Calculating Probabilities
Solutions can be found on page 6
1. Over a long period of time, the queue length of customers at the teller section of a major bank was observed to have the following probability distribution;
Number in queue
Probability
0
0.1
1
0.2
2
0.2
3
0.3
4 or more
0.2
Find the probability of
a. At most two people in the queue.
b. No more than three people in the queue.
c. At least one person in the queue.
d. Two or more people in the queue.
e. Given there is at least one person in the queue, what is the probability that there are 4 or more?
2. An airline has offered a special vacation package to Fiji. The length of stay is either for 3 days or 7 days, and the type of accommodation can be either economy, regular, or deluxe.
Consider the experiment of observing the choices made by the next person signing up for the package.
i.
How many experimental outcomes are possible?
ii. Draw a tree diagram for this experiment.
3. An investor has two stocks: stock A and stock B. Each stock may increase in value, decrease in value, or remain unchanged. Consider the experiment as the investment in both of the two stocks.
i.
How many experimental outcomes are possible?
ii. Draw a tree diagram for the experiment. iii. How many of the experimental outcomes result in an increase in value for at least one of the two stocks? iv. How many of the experimental outcomes result in an increase in value for both of the stocks?
4. Suppose that a manager of a large apartment complex provides the following subjective probability estimates about the number of vacancies that will exist next month:
Vacancies
0
1
2
3
4
5
Probability
.05
.15
.35
.25
.10
.10
List the components of each of the following events and calculate the probability of the events:
(a) No vacancies.
(b) At least four vacancies.
(c) Two or fewer vacancies.
5. The manager of a furniture store