Domanda del libro di testo
56. Defective Disks A pack of 100 recordable DVDs contains 5 defective disks. You select four disks. What is the probability of selecting at least three non defective disks?
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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
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Capitolo 3, Problema 3.4.17
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
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Determine whether the order of selection matters in the problem. Since the problem is about choosing 2 captains and the order in which they are chosen does not matter (e.g., Captain A and Captain B is the same as Captain B and Captain A), this situation involves combinations.
Recall the formula for combinations: C(n, r) = n! / [(r!)(n - r)!], where n is the total number of items to choose from, and r is the number of items to choose.
Identify the values of n and r in this problem. Here, n = 28 (the total number of players) and r = 2 (the number of captains to be chosen).
Substitute the values of n and r into the combination formula: C(28, 2) = 28! / [(2!)(28 - 2)!].
Simplify the expression by canceling out the common factorial terms in the numerator and denominator, leaving you with C(28, 2) = (28 × 27) / 2!.
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Permutations
Permutations refer to the arrangement of items where the order matters. For example, if you are selecting a president and a vice president from a group, the order in which you select them is important, as different roles imply different arrangements.
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07:11
Introduction to Permutations
Combinations
Combinations involve selecting items where the order does not matter. For instance, choosing 2 captains from a group of players means that selecting Player A and Player B is the same as selecting Player B and Player A; thus, the arrangement is irrelevant.
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05:22Combinations
Choosing from a Group
When determining how to choose from a group, it's essential to identify whether the selection involves distinct roles or positions. In this case, since the captains are not assigned specific roles beyond being captains, the situation is a combination, as the order of selection does not affect the outcome.
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08:50Z-Scores from Probabilities
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Domanda del libro di testo
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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Domanda del libro di testo
3. Explain why the statement is incorrect: The probability of rain is 150%.
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Domanda del libro di testo
Identifying Simple Events In Exercises 33-36, determine the number of outcomes in the event. Then decide whether the event is a simple event or not. Explain your reasoning.
34. A spreadsheet is used to randomly generate a number from 1 to 4000. Event B is generating a number less than 500.
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Domanda del libro di testo
"According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is
P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').
In Exercises 33–38, use Bayes’ Theorem to find P(A|B).
36. P(A) = 0.62, P(A') = 0.38, P(B|A) = 0.41 , and P(B|A') = 0.17 "
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Domanda del libro di testo
"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"
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