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

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

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2:01 minutes

Problem 3.1.34

Textbook Question

Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.
34. A spreadsheet is used to randomly generate a number from 1 to 4000. Event B is generating a number less than 500.

Verified step by step guidance

Step 1: Understand the problem. The spreadsheet generates a random number between 1 and 4000, inclusive. Event B is defined as generating a number less than 500. We need to determine the number of outcomes in Event B and decide if it is a simple event.

Step 2: Define the total sample space. The sample space consists of all possible outcomes, which are the integers from 1 to 4000. Therefore, the total number of outcomes in the sample space is 4000.

Step 3: Determine the number of outcomes in Event B. Event B includes all numbers less than 500. These numbers are the integers from 1 to 499. The number of outcomes in Event B is therefore 499.

Step 4: Define a simple event. A simple event is an event that consists of exactly one outcome. For example, generating the number 250 would be a simple event because it corresponds to a single outcome.

Step 5: Analyze whether Event B is a simple event. Since Event B consists of 499 outcomes (all numbers from 1 to 499), it is not a simple event. A simple event must have exactly one outcome, and Event B has multiple outcomes.

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Key Concepts

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

Simple Event

A simple event is an outcome or a combination of outcomes that cannot be broken down into simpler components. In probability, it refers to a single outcome from a sample space. For example, rolling a die and getting a '3' is a simple event, as it represents one specific outcome.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. In the context of generating a number from 1 to 4000, the sample space consists of all integers from 1 to 4000. Understanding the sample space is crucial for determining the total number of outcomes for any event.

Event

An event is a subset of the sample space that includes one or more outcomes. In this case, Event B, which is generating a number less than 500, includes all numbers from 1 to 499. An event can be simple (one outcome) or compound (multiple outcomes), and recognizing this distinction is key to analyzing probability.

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Textbook Question

Matching Probabilities In Exercises 11-16, match the event with its probability.

a. 0.95

b. 0.005

c. 0.25

d. 0

e. 0.375

f. 0.5

11. A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 153?

Textbook Question

Matching Probabilities In Exercises 11-16, match the event with its probability.

a. 0.95

b. 0.005

c. 0.25

d. 0

e. 0.375

f. 0.5

14. A game show contestant must randomly select a door. One door doubles her money while the other three doors leave her with no winnings. What is the probability she selects the

door that doubles her money?

Textbook Question

Identifying the Sample Space of a Probability Experiment In Exercises 25-32, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate.

25. Guessing the initial of a student's middle name

Textbook Question

28. Identifying a person's eye color (brown, blue, green, hazel, gray, other) and hair color (black, brown, blonde, red, other).

Textbook Question

Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.

43. Event C: rolling a number greater than 4

Textbook Question

Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.

46. Event F: rolling a number divisible by 5

Textbook Question

Boy or Girl? In Exercises 71-74, a couple plans to have three children. Each child is equally likely to be a boy or a girl.

71. What is the probability that all three children are girls?

Textbook Question

80. Unusual Events Can any of the events in Exercises 75-78 be considered unusual? Explain.

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Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.34. A spreadsheet is used to randomly generate a number from 1 to 4000. Event B is generating a number less than 500.

Key Concepts

Simple Event

Sample Space

Event

Watch next

Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.
34. A spreadsheet is used to randomly generate a number from 1 to 4000. Event B is generating a number less than 500.