Ch. 5 - Discrete Probability Distributions

Triola - Elementary Statistics 14th Edition

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Triola 14th Edition

Ch. 5 - Discrete Probability Distributions

Problem 5.2.28c

Chapter 5, Problem 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.

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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).

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.

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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