Probability and Odds (graded) The odds of winning a game are given as 1:25. What is the probability

Probability and Odds (graded)
The odds of winning a game are given as 1:25. What is the
probability that you will win this game? What is the probability that you will
lose this game? In your follow-up replies, consider which number in the odds
ratio needs to change and how it needs to change in order to increase the
probability of winning. (Note: See page 145 in the text for a discussion on
odds.)

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PLEASE COMPLETE THE QUIZ THIS WEEK that covers WEEK 1 and
WEEK 2 that covers Week 1 and Week 2 material only.

Here are a few questions that you can participate for
discussion points from your study plan on correlation and regression that may
help you toward understanding concepts and the quiz for Week 5. Please work on
only one question at a time. Answers are posted at the end of the questions.
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