Domanda del libro di testo
"In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.
21. Taking a driver's education course and passing the driver's license exam"
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Ch. 3 - Probability
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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TOC.tableOfContents
- 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: 9780137493470Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 3.RE.44
In Exercises 41-44, perform the indicated calculation.
44. (5C3)/(10C3)
Guida verificata passo dopo passo1
Step 1: Understand the problem. The problem involves calculating a ratio of combinations. Specifically, you need to compute \( \frac{{5C3}}{{10C3}} \), where \( nCk \) represents the number of ways to choose \( k \) items from \( n \) items without regard to order.
Step 2: Recall the formula for combinations. The formula for \( nCk \) is \( \binom{n}{k} = \frac{{n!}}{{k!(n-k)!}} \), where \( n! \) is the factorial of \( n \).
Step 3: Compute \( 5C3 \) using the formula. Substitute \( n = 5 \) and \( k = 3 \) into the formula: \( \binom{5}{3} = \frac{{5!}}{{3!(5-3)!}} = \frac{{5!}}{{3! \cdot 2!}} \). Simplify this expression.
Step 4: Compute \( 10C3 \) using the formula. Substitute \( n = 10 \) and \( k = 3 \) into the formula: \( \binom{10}{3} = \frac{{10!}}{{3!(10-3)!}} = \frac{{10!}}{{3! \cdot 7!}} \). Simplify this expression.
Step 5: Divide the results of \( 5C3 \) and \( 10C3 \). Use the simplified values from Steps 3 and 4 to compute \( \frac{{5C3}}{{10C3}} \). Simplify the fraction to get the final result.
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Combinations
Combinations refer to the selection of items from a larger set where the order does not matter. The notation 'nCr' represents the number of ways to choose 'r' items from 'n' items, calculated using the formula n! / (r!(n-r)!), where '!' denotes factorial. Understanding combinations is essential for solving problems involving group selections.
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05:22
Combinations
Factorial
A factorial, denoted as 'n!', is the product of all positive integers up to 'n'. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are fundamental in combinatorial calculations, as they help determine the total arrangements or selections of items in various scenarios.
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05:22Combinations
Probability
Probability is a measure of the likelihood of an event occurring, expressed as a ratio of favorable outcomes to the total number of possible outcomes. In the context of combinations, the ratio of two combinations, such as (5C3)/(10C3), can represent the probability of selecting a specific group from a larger set, providing insights into comparative likelihoods.
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5:37Introduction to Probability
Pratica correlata
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In Exercises 1-4, identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram when appropriate.
3. Experiment: Choosing a month of the year
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Domanda del libro di testo
In Exercises 25 and 26, determine whether the events are mutually exclusive. Explain your reasoning.
25. Event A: Randomly select a red jelly bean from a jar.
Event B: Randomly select a yellow jelly bean from the jar.
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Domanda del libro di testo
In Exercises 41-44, perform the indicated calculation.
42. 8P6
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Domanda del libro di testo
Telephone Numbers The telephone numbers for a region of Pennsylvania have an area code of 570. The next seven digits represent the local telephone numbers for that region. These cannot begin with a 0 or 1. In Exercises 15 and 16, assume your cousin lives within the given area code.
16. What is the probability of not randomly generating your cousin's telephone number on the first try?
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Domanda del libro di testo
In Exercises 19-22, determine whether the events are independent or dependent. Explain your reasoning.
19. Tossing a coin four times and getting four heads, and then tossing it a fifth time and getting a head
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