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Suppose that a book of 300 pages contains 30 printing mistakes. Assume that these errors are randomly distributed throughout the book. The number of errors per page has a Poisson’s distribution. What is the probability that 20 pages selected at random will be free from errors?
- a)0.205
- b)0.135
- c)0.1
- d)0.9
Correct answer is option 'B'. Can you explain this answer?
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Suppose that a book of 300 pages contains 30 printing mistakes. Assume...
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Suppose that a book of 300 pages contains 30 printing mistakes. Assume...
The Problem
We are given a book of 300 pages that contains 30 printing mistakes. These errors are randomly distributed throughout the book and the number of errors per page follows a Poisson's distribution. We need to find the probability that 20 pages selected at random will be free from errors.
Solution
To solve this problem, we can use the Poisson distribution formula. The Poisson distribution is used to describe the probability of a given number of events occurring in a fixed interval of time or space.
The formula for the Poisson distribution is:
P(x; λ) = (e^(-λ) * λ^x) / x!
Where:
- P(x; λ) is the probability of x events occurring in the given interval,
- e is the base of the natural logarithm (approximately 2.71828),
- λ is the average number of events that occur in the interval,
- x is the actual number of events that occur in the interval, and
- x! is the factorial of x.
In this problem, the average number of errors per page is given as λ = 30/300 = 0.1. We want to find the probability that 20 pages selected at random will be free from errors, so we need to find P(x = 0; λ).
Calculating the Probability
Using the Poisson distribution formula, we can calculate the probability as follows:
P(x = 0; λ) = (e^(-λ) * λ^0) / 0!
= e^(-λ) / 1
= e^(-0.1)
Using a calculator or a mathematical software, we can find that e^(-0.1) is approximately 0.9048.
Therefore, the probability that 20 pages selected at random will be free from errors is approximately 0.9048.
Answer
The correct answer is option B) 0.135.
We are given a book of 300 pages that contains 30 printing mistakes. These errors are randomly distributed throughout the book and the number of errors per page follows a Poisson's distribution. We need to find the probability that 20 pages selected at random will be free from errors.
Solution
To solve this problem, we can use the Poisson distribution formula. The Poisson distribution is used to describe the probability of a given number of events occurring in a fixed interval of time or space.
The formula for the Poisson distribution is:
P(x; λ) = (e^(-λ) * λ^x) / x!
Where:
- P(x; λ) is the probability of x events occurring in the given interval,
- e is the base of the natural logarithm (approximately 2.71828),
- λ is the average number of events that occur in the interval,
- x is the actual number of events that occur in the interval, and
- x! is the factorial of x.
In this problem, the average number of errors per page is given as λ = 30/300 = 0.1. We want to find the probability that 20 pages selected at random will be free from errors, so we need to find P(x = 0; λ).
Calculating the Probability
Using the Poisson distribution formula, we can calculate the probability as follows:
P(x = 0; λ) = (e^(-λ) * λ^0) / 0!
= e^(-λ) / 1
= e^(-0.1)
Using a calculator or a mathematical software, we can find that e^(-0.1) is approximately 0.9048.
Therefore, the probability that 20 pages selected at random will be free from errors is approximately 0.9048.
Answer
The correct answer is option B) 0.135.
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Suppose that a book of 300 pages contains 30 printing mistakes. Assume that these errors are randomly distributed throughout the book. The number of errors per page has a Poisson’s distribution. What is the probability that 20 pages selected at random will be free from errors?a)0.205b)0.135c)0.1d)0.9Correct answer is option 'B'. Can you explain this answer?
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Suppose that a book of 300 pages contains 30 printing mistakes. Assume that these errors are randomly distributed throughout the book. The number of errors per page has a Poisson’s distribution. What is the probability that 20 pages selected at random will be free from errors?a)0.205b)0.135c)0.1d)0.9Correct answer is option 'B'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Suppose that a book of 300 pages contains 30 printing mistakes. Assume that these errors are randomly distributed throughout the book. The number of errors per page has a Poisson’s distribution. What is the probability that 20 pages selected at random will be free from errors?a)0.205b)0.135c)0.1d)0.9Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose that a book of 300 pages contains 30 printing mistakes. Assume that these errors are randomly distributed throughout the book. The number of errors per page has a Poisson’s distribution. What is the probability that 20 pages selected at random will be free from errors?a)0.205b)0.135c)0.1d)0.9Correct answer is option 'B'. Can you explain this answer?.
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