Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

4. Probability

Multiplication Rule: Dependent Events

Statistics

4. Probability

Multiplication Rule: Dependent Events

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1:31 minutes

Problem 3.RE.22

Textbook Question

In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.
22. Getting high grades and being awarded an academic scholarship

Verified step by step guidance

Understand the definition of independent and dependent events: Two events are independent if the occurrence of one event does not affect the probability of the other event occurring. Conversely, two events are dependent if the occurrence of one event affects the probability of the other event occurring.

Identify the two events in the problem: Event A is 'getting high grades,' and Event B is 'being awarded an academic scholarship.'

Analyze the relationship between the two events: Consider whether achieving high grades (Event A) influences the likelihood of being awarded an academic scholarship (Event B).

Recognize that academic scholarships are often awarded based on academic performance, which means that getting high grades (Event A) increases the probability of being awarded a scholarship (Event B).

Conclude that the events are dependent because the occurrence of Event A (getting high grades) directly affects the likelihood of Event B (being awarded an academic scholarship).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Independent Events

Independent events are those whose outcomes do not affect each other. In probability, two events A and B are independent if the occurrence of A does not change the probability of B occurring, and vice versa. For example, flipping a coin and rolling a die are independent events because the result of one does not influence the other.

Dependent Events

Dependent events are those where the outcome of one event affects the outcome of another. In probability, two events A and B are dependent if the occurrence of A changes the probability of B occurring. For instance, drawing cards from a deck without replacement is a classic example of dependent events, as the first draw affects the composition of the deck for the second draw.

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which represents the probability of event A occurring given that event B has occurred. Understanding conditional probability is crucial for determining whether events are independent or dependent, as it helps assess how the occurrence of one event influences the likelihood of another.

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Textbook Question

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

23. Celebrities as Role Models In a sample of 1103 probable voters, three out of four say they would like entertainers to address social and political issues. Two probable voters are selected at random. (Source: The Hollywood Reporter)

a. Find the probability that both probable voters would like entertainers to address social and political issues.

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Textbook Question

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

29. In Vitro Fertilization In a recent year, about 1.9% of all infants born in the U.S. were conceived through assisted reproductive technology (ART). Of the ART deliveries, about 26.4% resulted in multiple births. (Source: Morbidity and Mortality Weekly Report)

a. Find the probability that a randomly selected infant was conceived through ART and was part of a multiple birth.

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Textbook Question

Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

30. Standardized Test Scores According to a survey, 57.8% of college-seeking high school seniors say they have taken one of the standardized tests for potential college students. Of these, 35.6% say they do not plan to submit their score with their college applications. (Adapted from Niche)

b. Find the probability that a randomly selected college-seeking high school senior took one of the standardized tests and plans to submit this score with their college

applications.

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Textbook Question

4. Determine whether the events are mutually exclusive. Then determine whether the events are independent or dependent. Explain your reasoning.

Event A: A bowler having the highest game in a 40-game tournament

Event B: Losing the bowling tournament

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Multiple Choice

What is the probability that a card player draws two aces from a standard deck of 52 cards if they keep the first card after drawing it?

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Multiple Choice

A library has chosen to select the two monthly book club reads by randomly choosing two books from a list of top 100 adult reads posted in the local newspaper. On the list, 62 books are fiction and 38 books are nonfiction. What is the probability of choosing two nonfiction books for this month's book club meeting?

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Multiple Choice

About 15% of people in a town have both a cat and a dog. As 64% of residents have a dog, what is the probability that someone in the town owns a cat, given they have a dog?

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Textbook Question

"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.

b. Find the probability that neither probable voter would like entertainers to address social and political issues."

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