Textbook Question
2. Determine whether each number could represent the probability of an event. Explain your reasoning. c. 2.3
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 3.3.17c
17. Selecting a Card A card is selected at random from a standard deck of 52 playing cards. Find the probability of each event.
c. Randomly selecting a 9 or a face card
Verified step by step guidance1
Step 1: Understand the problem. A standard deck of 52 playing cards consists of 4 suits (hearts, diamonds, clubs, spades), each containing 13 cards. The goal is to calculate the probability of randomly selecting either a 9 or a face card (Jack, Queen, King).
Step 2: Determine the total number of favorable outcomes. There are 4 nines in the deck (one for each suit) and 12 face cards (Jack, Queen, King, each appearing in all 4 suits). Add these together to find the total number of favorable outcomes: 4 (nines) + 12 (face cards) = 16.
Step 3: Recall the formula for probability. The probability of an event is given by the formula: . In this case, the total number of outcomes is the total number of cards in the deck, which is 52.
Step 4: Substitute the values into the formula. Use the favorable outcomes (16) and total outcomes (52) to calculate the probability: .
Step 5: Simplify the fraction if necessary. To express the probability in its simplest form, divide the numerator and denominator by their greatest common divisor (GCD). This step ensures the fraction is reduced to its lowest terms.
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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. In the context of selecting a card from a deck, it quantifies how many favorable outcomes exist compared to the total number of possible outcomes. For example, if there are 4 nines and 12 face cards in a deck, the probability of selecting either is calculated by dividing the number of favorable outcomes by the total number of cards.
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Favorable Outcomes
Favorable outcomes refer to the specific results that satisfy the conditions of the event being analyzed. In this case, the favorable outcomes for selecting a 9 or a face card include the 4 nines and the 12 face cards (Jack, Queen, King). Understanding how to identify and count these outcomes is crucial for calculating the overall probability of the event.
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06:00The Binomial Experiment
Total Outcomes
Total outcomes represent the complete set of possible results in a probability scenario. For a standard deck of 52 playing cards, the total outcomes are simply the total number of cards in the deck. This concept is essential for determining the probability, as it serves as the denominator in the probability formula, allowing for the comparison of favorable outcomes to the overall possibilities.
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Related Practice
Textbook Question
"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
24. Knowing a Person Who Was Murdered In a sample of 11,771 children ages 2 to 17, 8% have lost a friend or relative to murder. Four children are selected at random. (Adapted from University of New Hampshire)
c. Find the probability that at least one of the four has lost a friend or relative to murder."
Textbook Question
"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
23. Celebrities as Role Models In a sample of 1103 probable voters, three out of four say they would like entertainers to address social and political issues. Two probable voters are selected at random. (Source: The Hollywood Reporter)
c. Find the probability that at least one of the two probable voters would like entertainers to address social and political issues."
Textbook Question
19. U.S. Age Distribution The projected percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event. (Source: U.S. Census
Bureau)
c. Randomly selecting someone who is not 60 years or over
Textbook Question
81. Genetics A Punnett square is a diagram that shows all possible gene combinations in a cross of parents whose genes are known. When two pink snapdragon flowers (RW) are crossed, there are four equally likely possible outcomes for the genetic makeup of the offspring: red (RR), pink (RW), pink (WR), and white (WW), as shown in the Punnett square at the left. When two pink snapdragons are crossed, what is the probability that the offspring will be (c) white?
Textbook Question
23. Engineering Degrees The table shows the numbers of male and female students in the U.S. who received B.S. degrees in engineering in a recent year. A student earning a B.S. degree in engineering during that year is selected at random. Find the probability of each event.
(Source: National Center for Educational Statistics)
c. The student is not female or did not receive a mechanical engineering degree.