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 25m
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

Basic Concepts of Probability

Statistics

4. Probability

Basic Concepts of Probability

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1:23 minutes

Problem 3.1.11

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?

Verified step by step guidance

Step 1: Understand the problem. The question asks for the probability of selecting the number 153 using a random number generator that selects numbers from 1 to 100. This involves understanding the concept of probability and the total possible outcomes.

Step 2: Recall the formula for probability. The probability of an event occurring is given by the formula:

P = \frac{favorable \, outcomes}{total \, outcomes}

Step 3: Identify the favorable outcomes. In this case, the favorable outcome is selecting the number 153. However, note that the random number generator only selects numbers from 1 to 100, so 153 is not within the range of possible outcomes.

Step 4: Determine the total outcomes. The total number of outcomes is the range of numbers the generator can select, which is 100 (numbers 1 through 100).

Step 5: Conclude the probability. Since 153 is not within the range of possible outcomes, the probability of selecting 153 is 0. This corresponds to option 'd. 0' in the list of probabilities.

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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. A probability of 0 indicates an impossible event, while a probability of 1 indicates a certain event. In this context, understanding how to calculate the probability of selecting a specific number from a defined range is crucial.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. For the random number generator selecting a number from 1 to 100, the sample space consists of the integers 1 through 100. Recognizing the sample space helps in determining the total number of outcomes when calculating probabilities.

Event

An event is a specific outcome or a set of outcomes from the sample space. In this case, the event is selecting the number 153. Since 153 is not included in the sample space of numbers from 1 to 100, understanding the distinction between events and outcomes is essential for accurately assessing the probability.

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Textbook Question

2. Determine whether each number could represent the probability of an event. Explain your reasoning. c. 2.3

Textbook Question

2. Determine whether each number could represent the probability of an event. Explain your reasoning. d. -0.0004

Textbook Question

3. Explain why the statement is incorrect: The probability of rain is 150%.

Textbook Question

True or False? In Exercises 7-10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

9. A probability of 1/10 indicates an unusual event.

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

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.

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