Textbook Question
56. Defective Disks A pack of 100 recordable DVDs contains 5 defective disks. You select four disks. What is the probability of selecting at least three non defective disks?
Ch. 3 - Probability
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 3, Problem 3.1.34
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 guidance1
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.
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Probability of Multiple Independent Events
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.
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05:11Sampling Distribution of Sample Proportion
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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Related Practice
Textbook Question
3. Explain why the statement is incorrect: The probability of rain is 150%.
Textbook Question
Using a Tree Diagram In Exercises 67-70, a probability experiment consists of rolling a six-sided die and spinning the spinner shown at the left. The spinner is equally likely to land on each color. Use a tree diagram to find the probability of the event. Then explain whether the event can be considered unusual.
68. Event B: rolling an odd number and the spinner landing on green
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)."
Textbook Question
"According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is
P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').
In Exercises 33–38, use Bayes’ Theorem to find P(A|B).
36. P(A) = 0.62, P(A') = 0.38, P(B|A) = 0.41 , and P(B|A') = 0.17 "
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Textbook Question
In Exercises 15-18, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning.
17. The number of ways 2 captains can be chosen from 28 players on a lacrosse team