Textbook Question
In Exercises 45-48, use combinations and permutations.
48. An employer must hire 2 people from a list of 13 applicants. In how many ways can the employer choose to hire the two people?
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.RE.11
In Exercises 7-12, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning.
11. The probability of rolling 2 six-sided dice and getting a sum of 9 is 1/9.
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Step 1: Understand the three types of probability: Classical probability is based on theoretical reasoning and assumes equally likely outcomes. Empirical probability is based on observed data or experiments. Subjective probability is based on personal judgment or opinion.
Step 2: Analyze the given statement. The problem states that the probability of rolling two six-sided dice and getting a sum of 9 is 1/9. This probability is derived from theoretical reasoning about the possible outcomes of rolling two dice.
Step 3: Recall that classical probability is calculated using the formula: . In this case, the favorable outcomes are the combinations of dice rolls that result in a sum of 9, and the total outcomes are all possible combinations of rolling two dice.
Step 4: Determine whether the probability is based on theoretical reasoning or observed data. Since the probability is calculated using the theoretical number of favorable outcomes divided by the total number of outcomes, it is an example of classical probability.
Step 5: Conclude that the statement is an example of classical probability because it is derived from theoretical calculations rather than experimental data or personal judgment.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Classical Probability
Classical probability is based on the assumption that all outcomes in a sample space are equally likely. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, when rolling two six-sided dice, the total number of outcomes is 36, and the number of ways to achieve a sum of 9 can be counted, leading to a probability calculation.
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Empirical Probability
Empirical probability is determined through experimentation or observation rather than theoretical calculations. It is calculated by taking the ratio of the number of times an event occurs to the total number of trials conducted. This type of probability is useful when theoretical probabilities are difficult to ascertain or when real-world data is available.
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Subjective Probability
Subjective probability is based on personal judgment, intuition, or experience rather than on exact calculations or empirical data. It reflects an individual's belief about the likelihood of an event occurring. This type of probability can vary significantly between individuals and is often used in situations where statistical data is limited or unavailable.
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Related Practice
Textbook Question
In Exercises 33 and 34, use the pie chart at the left, which shows the percent distribution of the number of students in U.S. public schools in a recent year. (Source: U.S. National Center for Education Statistics)
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34. Find the probability of randomly selecting a school with 300 or more students.
Textbook Question
"In Exercises 17 and 18, use the table, which shows the numbers of first-time and repeat U.S. nursing students taking the National Council Licensure Examination (NCLEX-RN® exam) to pass or fail in a recent year. (Adapted from National Council Licensure Examinations)
18. Find the probability that a student passed, given that the student repeated the exam."
Textbook Question
28. A sample of 6500 automobiles found that 1560 of the automobiles were black, 3120 of the automobiles were sedans, and 1170 of the automobiles were black sedans. Find the probability that a randomly chosen automobile from this sample is black or a sedan.
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Textbook Question
In Exercises 5 and 6, use the Fundamental Counting Principle.
6. The state of Virginia's license plates have three letters and four digits. Assuming that any letter or digit can be used, how many different license plates are possible?
Textbook Question
In Exercises 49-53, use counting principles to find the probability.
53. A corporation has six male senior executives and four female senior executives. Four senior executives are chosen at random to attend a technology seminar. What is the
probability of choosing
b. four women?