Problem

Based on a poll, among adults who regret getting tattoos, $13 \%$ say that they were too young when they got their tattoos. Assume that nine adults who regret getting tattoos are randomly selected, and find the indicated probability. Complete parts (a) through (d) below. a. Find the probability that none of the selected adults say that they were too young to get tattoos. (Round to four decimal places as needed.) b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos. (Round to four decimal places as needed.) c. Find the probability that the number of selected adults saying they were too young is 0 or 1 . (Round to four decimal places as needed.) d. If we randomly select nine adults, is 1 a significantly low number who say that they were too young to get tattoos? because the probability that of the selected adults say that they were too young is

Solution

Step 1 :The problem is asking for the probability of certain outcomes when selecting nine adults who regret getting tattoos. The outcomes are based on whether they believe they were too young when they got their tattoos. This is a binomial probability problem, where each trial (selecting an adult) is independent and has two possible outcomes (they believe they were too young or they don't). The probability of success (they believe they were too young) is given as 13%.

Step 2 :For part a, we need to find the probability that none of the selected adults say that they were too young to get tattoos. This is equivalent to 9 failures in a row. The formula for binomial probability is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\) where: \(P(X=k)\) is the probability of k successes in n trials, \(C(n, k)\) is the number of combinations of n items taken k at a time, p is the probability of success on each trial, n is the number of trials, and k is the number of successes.

Step 3 :In this case, n=9 (the number of adults), p=0.13 (the probability an adult says they were too young), and k=0 (the number of adults who say they were too young). We can plug these values into the formula to find the answer.

Step 4 :\(n = 9\)

Step 5 :\(p = 0.13\)

Step 6 :\(k = 0\)

Step 7 :\(combinations = 1\)

Step 8 :\(probability = 0.28554415424302954\)

Step 9 :Final Answer: The probability that none of the selected adults say that they were too young to get tattoos is approximately \(\boxed{0.2855}\).

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Source: https://solvelyapp.com/problems/19298/

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