Acrophobia USA Today reported results from a survey in which subjects were asked if they are afraid of heights in tall buildings. The results are summarized in the accompanying table. Does this table describe a probability distribution? Why or why not?
Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 53m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample2h 19m
- 10. Hypothesis Testing for Two Samples3h 22m
- 11. Correlation1h 6m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
5. Binomial Distribution & Discrete Random Variables
Binomial Distribution
Problem 5.2.28c
Textbook Question
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.

1
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).
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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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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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