Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

4. Probability

Addition Rule

Statistics

4. Probability

Addition Rule

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3:50 minutes

Problem 4.RE.4

Textbook Question

In Exercises 1–10, use the data in the accompanying table and express all results in decimal form. (The data are from “The Left-Handed: Their Sinister History,” by Elaine Fowler Costas, Education Resources Information Center, Paper 399519.)

Lefty or Female Find the probability of randomly selecting one of the study subjects and getting someone who writes with their left hand or is a female.

Verified step by step guidance

Step 1: Understand the problem. We are tasked with finding the probability of randomly selecting a study subject who either writes with their left hand or is a female. This involves using the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

Step 2: Calculate the total number of study subjects. Add all the values in the table: Total = 23 (Male Left-Handed) + 217 (Male Right-Handed) + 65 (Female Left-Handed) + 455 (Female Right-Handed).

Step 3: Calculate P(A), the probability of selecting someone who writes with their left hand. Add the number of left-handed males and females (23 + 65), then divide by the total number of study subjects.

Step 4: Calculate P(B), the probability of selecting someone who is female. Add the number of females (65 + 455), then divide by the total number of study subjects.

Step 5: Calculate P(A and B), the probability of selecting someone who is both female and writes with their left hand. This is simply the number of left-handed females (65) divided by the total number of study subjects. Finally, use the formula P(A or B) = P(A) + P(B) - P(A and B) to find the desired probability.

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Key Concepts

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

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the chance of randomly selecting a subject who either writes with their left hand or is female. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.

Union of Events

The union of events refers to the occurrence of at least one of two or more events. In this question, we are interested in the union of two events: selecting someone who writes with their left hand and selecting a female. The probability of the union can be calculated using the formula P(A or B) = P(A) + P(B) - P(A and B), where A and B are the two events.

Data Representation

Data representation involves organizing and displaying data in a way that makes it easy to analyze and interpret. In this case, the data is presented in a contingency table that categorizes subjects based on gender and whether they write with their left hand. Understanding how to read and interpret this table is crucial for calculating the required probabilities.

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Related Practice

Multiple Choice

A card is drawn from a standard deck of 52 cards. What is the probability that the card is a diamond or a king?

Textbook Question

In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive (incorrect) results; among 157 negative results, there are 3 false negative (incorrect) results. (Hint: Construct a table similar to Table 4-1.)

Testing for Marijuana Use

c. What is the probability that a randomly selected subject had a true negative result?

Textbook Question

Testing for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject tested positive or did not use marijuana.

Textbook Question

Exclusive Or The exclusive or means either one or the other event occurs, but not both.

If one of the high school drivers is randomly selected, find the probability of getting one who texted while driving or drove when drinking alcohol.

b. Repeat Exercise 11 “Texting or Drinking” using the exclusive or instead of the inclusive or.

Textbook Question

Testing for Marijuana Use

b. How many of the subjects had a true negative result?

Textbook Question

In Exercises 9–20, use the data in the following table, which lists survey results from high school drivers at least 16 years of age (based on data from “Texting While Driving and Other Risky Motor Vehicle Behaviors Among U.S. High School Students,” by O’Malley, Shults, and Eaton, Pediatrics, Vol. 131, No. 6). Assume that subjects are randomly selected from those included in the table. Hint: Be very careful to read the question correctly.

Texting or Drinking If one of the high school drivers is randomly selected, find the probability of getting one who texted while driving or drove when drinking alcohol.

Textbook Question

1. When two events are mutually exclusive, why is P(A and B) = 0?

Textbook Question

True or False? In Exercises 3-6, determine whether the statement is true or false. If it is false,

explain why.

4. When two events are independent, they are also mutually exclusive.

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