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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.1.94
Chapter 3, Problem 3.1.94

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.
94. A card is picked at random from a standard deck of 52 playing cards. Find the odds that it is a spade.

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Step 1: Understand the problem. A standard deck of 52 playing cards is divided into 4 suits: spades, hearts, diamonds, and clubs. Each suit contains 13 cards. We are tasked with finding the odds that a randomly picked card is a spade.
Step 2: Recall the formula for odds. The odds of an event occurring is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. Mathematically, this can be expressed as: Number of Successful OutcomesNumber of Unsuccessful Outcomes.
Step 3: Identify the successful outcomes. Since there are 13 spades in the deck, the number of successful outcomes is 13.
Step 4: Identify the unsuccessful outcomes. The total number of cards in the deck is 52, and the number of unsuccessful outcomes is the total number of cards minus the number of spades: 52-13.
Step 5: Write the odds. The odds of picking a spade are the ratio of successful outcomes (13) to unsuccessful outcomes (52 - 13). Simplify this ratio if possible to express the final odds in the form of 'a : b'.

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Key Concepts

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

Odds vs. Probability

Odds represent the ratio of successful outcomes to unsuccessful outcomes, while probability measures the likelihood of an event occurring out of all possible outcomes. For instance, if the odds of winning are 2:3, the probability of winning is calculated as the number of successful outcomes divided by the total number of outcomes, which in this case would be 2 out of 5.
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Standard Deck of Cards

A standard deck of playing cards consists of 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards. Understanding the composition of the deck is essential for calculating the odds of drawing a specific suit, such as spades, which directly influences the outcome of the problem presented.
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Calculating Odds

To calculate the odds of an event, you need to determine the number of successful outcomes and the number of unsuccessful outcomes. For example, if there are 13 spades in a deck of 52 cards, the odds of drawing a spade would be 13 successful outcomes to 39 unsuccessful outcomes, resulting in odds of 13:39, which can be simplified to 1:3.
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Related Practice
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.

32. Rolling a six-sided die, tossing two coins, and spinning the fair spinner shown

Textbook Question

Using the Fundamental Counting Principle In Exercises 37-40, use the Fundamental Counting Principle.

37. Menu A restaurant offers a \$15 dinner special that lets you choose from 6 appetizers, 12 entrées, and 8 desserts. How many different meals are available when you select an appetizer, an entrée, and a dessert?

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.

31. Rolling a pair of six-sided dice

Textbook Question

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

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

Textbook Question

"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.

10. A father having hazel eyes and a daughter having hazel eyes"