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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.1.11
Chapter 3, Problem 3.1.11

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
11. A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 153?

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1
Step 1: Understand the problem. The question asks for the probability of selecting the number 153 using a random number generator that selects numbers from 1 to 100. This involves understanding the concept of probability and the total possible outcomes.
Step 2: Recall the formula for probability. The probability of an event occurring is given by the formula: P=favorable \, outcomestotal \, outcomes.
Step 3: Identify the favorable outcomes. In this case, the favorable outcome is selecting the number 153. However, note that the random number generator only selects numbers from 1 to 100, so 153 is not within the range of possible outcomes.
Step 4: Determine the total outcomes. The total number of outcomes is the range of numbers the generator can select, which is 100 (numbers 1 through 100).
Step 5: Conclude the probability. Since 153 is not within the range of possible outcomes, the probability of selecting 153 is 0. This corresponds to option 'd. 0' in the list of probabilities.

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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. A probability of 0 indicates an impossible event, while a probability of 1 indicates a certain event. In this context, understanding how to calculate the probability of selecting a specific number from a defined range is crucial.
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Introduction to Probability

Sample Space

The sample space is the set of all possible outcomes of a random experiment. For the random number generator selecting a number from 1 to 100, the sample space consists of the integers 1 through 100. Recognizing the sample space helps in determining the total number of outcomes when calculating probabilities.
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Sampling Distribution of Sample Proportion

Event

An event is a specific outcome or a set of outcomes from the sample space. In this case, the event is selecting the number 153. Since 153 is not included in the sample space of numbers from 1 to 100, understanding the distinction between events and outcomes is essential for accurately assessing the probability.
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Related Practice
Textbook Question

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).

33. P(A) = 2/3, P(A') = 1/3, P(B|A) = 1/5 , and P(B|A') = 1/2

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Textbook Question

"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).

35. P(A) = 0.25, P(A') = 0.75, P(B|A) = 0.3 , and P(B|A') = 0.5 "

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Textbook Question

1. When two events are mutually exclusive, why is P(A and B) = 0?

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Textbook Question

Finding Classical Probabilities In Exercises 41-46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event.

43. Event C: rolling a number greater than 4

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Textbook Question

Classifying Events Based on Studies In Exercises 15-18, identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.

17. A study found that there is no relationship between playing violent video games and aggressive or bullying behavior in teenagers. (Source: The Royal Society Publishing)

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Textbook Question

Cards In Exercises 59-62, you are dealt a hand of five cards from a standard deck of 52 playing cards.

59. Find the probability of being dealt two clubs and one of each of the other three suits.

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