PROBABILITY DISTRIBUTIONS
Objective - CONCEPTS:
1. Determine which of the following numbers could not represent the probability of an event
0, 0.008, -0.6, 65%, 715/1206, 60/47
Study plan: 3.1.1, 3.1.2, 3.1.7, 3.1.8
Objective-Sample Space
2. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space.
Determining a person’s grade Freshman (F), Sophomore (So), Junior (J), Senior (Se) and gender (male(M) Female (F))
Study Plan: 3.1.15, 3.1.17, 3.1.19
Objective-Simple Events
3. Determine the number of outcomes in the event. Decide whether the event is a simple event or not.
You randomly select one card from a standard deck. Event A is selecting a red four.
Study Plan: 3.1.21, 3.1.23
Objective-Frequency Distribution
4. Use the frequency distribution below, which shows the number of voters (in millions) according to age, to find the probability that a voter chosen at random is in the given age range.
Not between 25 and 34 years old
Ages of voters
|
Frequency
|
18 to 20
|
7.4
|
21 to 24
|
11.5
|
25 to 34
|
21.8
|
35 to 44
|
25.5
|
45 to 64
|
56.8
|
65 and over
|
28.7
|
Study Plan: 3.1.55, 3.1.57, 3.1.59, 3.1.61, 3.1.63
Objective-Distinguish between independent and dependent events
5. Researchers found that people with depression are four times more likely to have a breathing-related sleep disorder that people who are not depressed. Identify the two events described in the study. Do the results indicate that the events are independent or dependent?
Study Plan: 3.2.7, 3.2.11, 3.2.13, 3.2.15
Objective-Conditional Probability
6. In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman in 600 carries a mutation of the BRCA gene. Seven out of 10 women with this mutation develop breast cancer.
a. Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.
b. Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer.
c. Are the events of carrying this mutation and developing breast cancer independent or dependent events.
Study Plan: 3.2.17, 3.2.27
Objective-Multiplication Rule to Find Probabilities
7. A study found that 38% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-two percent of the ART pregnancies resulted in multiple births.
a. Find the probability that a randomly selected ART cycle resulted in a pregnancy and produced a multiple birth.
b. Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth.
c. Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth? Explain
Study Plan: 3.2.21, 3.2.23, 3.2.26
Objective-Mutually exclusive
8. Decide if the events are mutually exclusive.
Event A: Randomly selecting someone treated with a certain medication.
Event B: Randomly selecting someone who received no medication
Study Plan: 3.3.7, 3.3.9, 3.3.11
Objective-Addition Rule
9. During a 52-Week period, a company paid overtime wages for 16 Weeks and hired temporary help for 8 Weeks. During 4 Weeks, the company paid overtime and hired temporary help.
a. Are the events “Selecting a Week that contained overtime wages” and “selecting a Week that contained temporary help wages” mutually exclusive
b. If an auditor randomly examined the payroll records for only one Week, what is the probability that the payroll for that Week contained Overtime wages or temporary help wages?
Study Plan: 3.3.13, 3.3.15, 3.3.17,3.3.25
Objective-Permutation and Combination
10. Find 37 C2
Study Plan: 3.4.8, 3.4.11, 3.4.13, 3.4.14
Objective-Counting Principles
11. A certain lottery has 30 numbers. In how many different ways can 5 of the numbers be selected? Assume that order of selection is not important
Study Plan: 3.4.21, 3.4.22, 3.4.23, 3.4.25
Objective-CONSTRUCT PROBABILTIES
12. A frequency distribution is shown below.
The number of dogs per household in a small town
Dogs 0 1 2 3 4 5
Households 1128 424 167 48 27 17
a. Use the frequency distribution to construct a probability distribution
x
|
P(x)
|
0
| |
1
| |
2
| |
3
| |
4
| |
5
|
b. Find the mean of the probability distribution
c. Find the variance of the probability distribution
d. Find the standard deviation of the probability distribution
Study Plan: 4.1.13, 4.1.15, 4.1.17, 4.1.19, 4.1.21, 4.1.23, 4.1.25, 4.1.27, 4.1.29, 4.1.31, 4.1.35, 4.1.37, 4.1.39
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