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Ch. 5 - Discrete Probability Distributions
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Triola 14th EditionCh. 5 - Discrete Probability Distributions문제 5.2.28c
5장, 문제 5.2.28c

In Exercises 25–28, find the probabilities and answer the questions.




Too Young to Tat Based on a Harris poll, among adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly selected, and find the indicated probability.


c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

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Step 1: Recognize that this is a binomial probability problem. The problem involves a fixed number of trials (n = 5), two possible outcomes (saying they were too young or not), and a constant probability of success (p = 0.20). The binomial probability formula is P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where k is the number of successes.
Step 2: To find the probability that the number of selected adults saying they were too young is 0 or 1, calculate P(X = 0) and P(X = 1) separately using the binomial probability formula.
Step 3: For P(X = 0), substitute k = 0, n = 5, and p = 0.20 into the formula: P(X = 0) = (5 choose 0) * (0.20)^0 * (1-0.20)^5. Simplify the expression to compute the probability.
Step 4: For P(X = 1), substitute k = 1, n = 5, and p = 0.20 into the formula: P(X = 1) = (5 choose 1) * (0.20)^1 * (1-0.20)^4. Simplify the expression to compute the probability.
Step 5: Add the probabilities from Step 3 and Step 4 to find the total probability: P(X = 0 or X = 1) = P(X = 0) + P(X = 1). This is the final result.

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주요 개념

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Binomial Probability

Binomial probability refers to the likelihood of a specific number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. In this context, the 'success' is defined as an adult saying they were too young when they got their tattoo, with a success probability of 20%. The binomial formula is used to calculate the probability of obtaining a certain number of successes (0 or 1 in this case) out of the total trials (5 adults).
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가이드 코스
06:39
Calculating Probabilities in a Binomial Distribution

Probability Distribution

A probability distribution describes how the probabilities are distributed over the values of a random variable. For a binomial distribution, it provides the probabilities of obtaining 0, 1, 2, ..., n successes in n trials. Understanding this distribution is crucial for calculating the probabilities of specific outcomes, such as the number of adults who regret their tattoos due to being too young.
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가이드 코스
06:39
Calculating Probabilities in a Binomial Distribution

Complement Rule

The complement rule in probability states that the probability of an event occurring is equal to 1 minus the probability of it not occurring. This concept is useful when calculating probabilities for multiple outcomes, such as finding the probability of 0 or 1 adults saying they were too young. By understanding the complement, one can simplify calculations by focusing on the opposite outcomes.
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Complementary Events
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e. If one of the challenges is randomly selected, find the probability that it was made by a man, given that the challenge was upheld with an overturned call.

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Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.



d. If 1 of the 945 challenges is randomly selected, find the probability that it was made by a man or was upheld with an overturned call.


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c. Find the probability of 40 or more first lines for Democrats.

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In Exercises 31 and 32, assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods (as in one of Mendel’s famous experiments).


Hybrids Assume that offspring peas are randomly selected in groups of 16.


c. Is a result of 7 peas with green pods a result that is significantly low? Why or why not?

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Salary Negotiations In a Jobvite survey, 2287 adult workers were randomly selected and asked about salary negotiations.


a. 29% of the respondents reported that they negotiated salary at their latest job. What is the number of respondents who reported that they negotiated salary?

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