Textbook Question
In Exercises 7-14, perform the indicated calculation.
12. (10C7)/(14C7)
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 3.1.36
"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.
36. You randomly select one card from a standard deck of 52 playing cards. Event B is selecting the ace of spades."
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Step 1: Understand the problem. A simple event is an event that consists of exactly one outcome. Here, Event B is selecting the ace of spades from a standard deck of 52 playing cards.
Step 2: Determine the total number of outcomes in the sample space. A standard deck of playing cards contains 52 cards, so the sample space has 52 possible outcomes.
Step 3: Identify the number of outcomes in Event B. Event B specifies selecting the ace of spades, which is a single card. Therefore, Event B consists of exactly one outcome.
Step 4: Decide whether Event B is a simple event. Since Event B consists of only one outcome (selecting the ace of spades), it qualifies as a simple event.
Step 5: Explain the reasoning. A simple event is defined as an event with exactly one outcome. Event B meets this criterion because it involves selecting only one specific card, the ace of spades, from the deck.
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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, drawing one specific card from a deck, such as the ace of spades, is a simple event because it represents one distinct 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 drawing a card from a standard deck, the sample space consists of 52 unique cards. Understanding the sample space is crucial for determining the total number of outcomes and for calculating probabilities associated with events.
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05:11Sampling Distribution of Sample Proportion
Counting Outcomes
Counting outcomes involves determining the number of possible results for a given event. In this case, selecting the ace of spades from a deck of cards has only one favorable outcome. This concept is essential for evaluating whether an event is simple and for calculating probabilities, as it helps quantify the likelihood of specific events occurring.
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Related Practice
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
23. Footrace There are 72 runners in a 10-kilometer race. How many ways can the runners finish first, second, and third?
Textbook Question
3. What does the notation P(B|A) mean?
Textbook Question
Odds The chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For example, when the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of winning are 2 : 3 (read "2 to 3"). In Exercises 91-96, use this information about odds.
92. The probability of winning an instant prize game is 1/10. The odds of winning a different instant prize game are 1 : 10. You want the best chance of winning. Which game should you play? Explain your reasoning.
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