Textbook Question
Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
20. Coin and Die A coin is tossed and a die is rolled. Find the probability of tossing a tail and then rolling a number greater than 2.
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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 3.4.53
Warehouse In Exercises 51-54, a warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be
interviewed about the work environment.
Find the probability of choosing four third-shift workers.
Verified step by step guidance1
Step 1: Identify the total number of workers in the warehouse. Add the workers from all shifts: 24 (first shift) + 17 (second shift) + 13 (third shift). This gives the total population size (N).
Step 2: Determine the number of workers on the third shift (k), which is 13, and the total number of workers to be chosen (n), which is 8.
Step 3: Use the hypergeometric probability formula to calculate the probability of choosing exactly 4 third-shift workers. The formula is: P(X = x) = (C(k, x) * C(N-k, n-x)) / C(N, n), where C(a, b) represents the combination formula a! / (b!(a-b)!).
Step 4: Substitute the values into the formula. Here, k = 13, N = 54, n = 8, and x = 4. Compute the combinations: C(13, 4) for selecting 4 third-shift workers, C(41, 4) for selecting the remaining 4 workers from the other shifts, and C(54, 8) for selecting any 8 workers from the total population.
Step 5: Simplify the expression by calculating each combination and dividing the result of the numerator by the denominator. This will give the probability of choosing exactly 4 third-shift workers.
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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 this context, it involves calculating the chance of selecting a specific number of third-shift workers from a total group of workers. Understanding how to compute probabilities is essential for solving problems related to random selection.
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Introduction to Probability
Combinations
Combinations refer to the selection of items from a larger set where the order does not matter. In this scenario, we need to determine how many ways we can choose four third-shift workers from the total number of third-shift workers available. The formula for combinations is crucial for calculating the total possible selections.
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05:22Combinations
Total Workers and Distribution
Understanding the total number of workers and their distribution across shifts is vital for calculating probabilities. In this case, there are 54 workers in total (24 first shift, 17 second shift, and 13 third shift). This distribution helps in determining the total number of ways to select workers and the specific group of interest (third-shift workers).
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Guided course
06:38Intro to Frequency Distributions
Related Practice
Textbook Question
Using a Frequency Distribution to Find Probabilities In Exercises 49-52, use the frequency distribution at the left, which shows the population of the United States by age group, to find the probability that a U.S. resident chosen at random is in the age range. (Source: U.S. Census Bureau)
52. 65 years old and older
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Textbook Question
Matching Probabilities In Exercises 11-16, match the event with its probability.
a. 0.95
b. 0.005
c. 0.25
d. 0
e. 0.375
f. 0.5
16. You toss a coin four times. What is the probability of tossing tails exactly half of the time?
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Textbook Question
80. Unusual Events Can any of the events in Exercises 75-78 be considered unusual? Explain.
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Textbook Question
In Exercises 7-14, perform the indicated calculation.
12. (10C7)/(14C7)
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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.
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