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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1:50 minutes

Problem 3.2.10

Textbook Question

"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.
10. A father having hazel eyes and a daughter having hazel eyes"

Verified step by step guidance

Step 1: Understand the concept of independent and dependent events. Independent events are those where the occurrence of one event does not affect the probability of the other event. Dependent events are those where the occurrence of one event does affect the probability of the other event.

Step 2: Analyze the relationship between the father having hazel eyes and the daughter having hazel eyes. Consider whether the genetic inheritance of eye color plays a role in determining the probability of the daughter having hazel eyes.

Step 3: Recall that eye color is influenced by genetics. A father having hazel eyes increases the likelihood of the daughter inheriting hazel eyes due to shared genetic traits. This suggests a dependency between the two events.

Step 4: Formulate the reasoning: Since the probability of the daughter having hazel eyes is affected by the father’s eye color (due to genetic inheritance), these events are dependent.

Step 5: Conclude that the events are dependent and explain that the dependency arises from the genetic relationship between the father and daughter, which influences the likelihood of shared traits like eye color.

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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 creates dependent events, as the first draw alters the composition of the deck for the second draw.

Genetic Inheritance

Genetic inheritance refers to the way traits and characteristics are passed from parents to offspring through genes. In the context of the question, the eye color of a father and daughter can be influenced by their genetic makeup, which may indicate a dependent relationship. The probability of the daughter having hazel eyes is affected by the father's eye color, illustrating how genetic traits can be interrelated.

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Related Practice

Textbook Question

"1. What is the difference between independent and dependent events?

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Textbook Question

"2. Give an example of

a. two events that are independent.

b. two events that are dependent."

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Textbook Question

"True or False? In Exercises 5 and 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

5. If two events are independent, then P(A|B) = P(B)."

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Textbook Question

"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.

9. Selecting a king from a standard deck of 52 playing cards, replacing it, and then selecting a queen from the deck"

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Textbook Question

"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.

12. Not putting money in a parking meter and getting a parking ticket"

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Textbook Question

"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.

13. Rolling a six-sided die and then rolling the die a second time so that the sum of the two rolls is five"

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Textbook Question

"Classifying Events Based on Studies In Exercises 15-18, identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.

15. A study was conducted to debunk the idea that abilities in music and math are related. Instead, the study showed a strong relationship between achievements in music and math.

(Source: University of Kansas)"

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Textbook Question

"Classifying Events Based on Studies In Exercises 15-18, identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.

16. A study found no significant association between the use of talc powder and the incidence of ovarian cancer in women. (Source: JAMA)"

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"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.10. A father having hazel eyes and a daughter having hazel eyes"

Key Concepts

Independent Events

Dependent Events

Genetic Inheritance

Watch next

"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.
10. A father having hazel eyes and a daughter having hazel eyes"