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

Addition Rule

Statistics

4. Probability

Addition Rule

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2:33 minutes

Problem 3.3.26a

Textbook Question

26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.
a. The person wears only contacts or only glasses.

Verified step by step guidance

Step 1: Identify the relevant data from the table. The table provides the number of people who wear only contacts, only glasses, both, or neither. To find the probability of a person wearing only contacts or only glasses, focus on the 'Only contacts' and 'Only glasses' columns.

Step 2: Add the total number of people who wear only contacts and only glasses. From the table, the total for 'Only contacts' is 253, and the total for 'Only glasses' is 1268. Add these values together to get the total number of people who wear either only contacts or only glasses.

Step 3: Determine the total number of people surveyed. From the table, the total number of people surveyed is 3203.

Step 4: Calculate the probability of the event. The probability is calculated as the ratio of the number of people who wear only contacts or only glasses to the total number of people surveyed. Use the formula: \( P = \frac{\text{Number of people wearing only contacts or only glasses}}{\text{Total number of people surveyed}} \).

Step 5: Simplify the fraction obtained in Step 4 to express the probability in its simplest form or as a decimal, if required.

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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 an event will occur, expressed as a number between 0 and 1. In this context, it involves calculating the chance of randomly selecting a person who wears only contacts or only glasses from the total surveyed population. The probability can be determined by dividing the number of favorable outcomes by the total number of outcomes.

Mutually Exclusive Events

Mutually exclusive events are events that cannot occur at the same time. In this survey, wearing only contacts and wearing only glasses are mutually exclusive; a person cannot wear both at the same time. Understanding this concept is crucial for accurately calculating the probability of selecting someone who wears either only contacts or only glasses.

Total Outcomes

Total outcomes refer to the complete set of possible results in a probability scenario. In this case, the total number of surveyed individuals is 3203, which serves as the denominator when calculating probabilities. Knowing the total outcomes is essential for determining the probability of specific events, such as wearing only contacts or only glasses.

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Related Practice

Textbook Question

17. Selecting a Card A card is selected at random from a standard deck of 52 playing cards. Find the probability of each event.

c. Randomly selecting a 9 or a face card

Textbook Question

18. Rolling a Die You roll a die. Find the probability of each event.

b. Rolling a 2 or an odd number

Textbook Question

Mental Health A survey asks 4805 parents the severity of the mental issues they experienced from the coronavirus pandemic. The results are shown in the table. A parent is randomly selected from the sample. Find the probability of each event. (Adapted from Kaiser Family Foundation)

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c. The parent did not have major mental health issues or is a mother.

Textbook Question

25. Working from Home The table shows the results of a survey that asked 1811 people how often they work from home. A person is selected at random from the sample. Find the probability of each event.

b. The person is female or does not work from home.

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Textbook Question

26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.

d. The person is male or does not wear glasses.

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Textbook Question

29. Explain, in your own words, why in the Addition Rule for P(A or B or C), P(A and B and C) is added at the end of the formula.

Textbook Question

In Exercises 25 and 26, determine whether the events are mutually exclusive. Explain your reasoning.

25. Event A: Randomly select a red jelly bean from a jar.

Event B: Randomly select a yellow jelly bean from the jar.

Textbook Question

28. A sample of 6500 automobiles found that 1560 of the automobiles were black, 3120 of the automobiles were sedans, and 1170 of the automobiles were black sedans. Find the probability that a randomly chosen automobile from this sample is black or a sedan.

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26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.a. The person wears only contacts or only glasses.

Key Concepts

Probability

Mutually Exclusive Events

Total Outcomes

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26. Eye Survey The table shows the results of a survey that asked 3203 people whether they wore contacts or glasses. A person is selected at random from the sample. Find the probability of each event.
a. The person wears only contacts or only glasses.