Based on a poll, among adults who regret getting tattoos, \( 20 \% \) 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. 0.1342 (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. 0.3020 (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 . \( \square \) (Round to four decimal places as needed.)

To solve these problems, we can use the binomial probability formula, which is given by: \[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \] where: - \( n \) is the number of trials (in this case, 9 adults), - \( k \) is the number of successes (the number of adults who say they were too young), - \( p \) is the probability of success (in this case, \( 0.20 \)), - \( \binom{n}{k} \) is the binomial coefficient, calculated as \( \frac{n!}{k!(n-k)!} \). Given that \( p = 0.20 \) and \( n = 9 \), we can calculate the probabilities for parts (a), (b), and (c). ### Part (a) **Find the probability that none of the selected adults say that they were too young to get tattoos.** Here, \( k = 0 \): \[ P(X = 0) = \binom{9}{0} (0.20)^0 (0.80)^9 \] Calculating this: \[ \binom{9}{0} = 1 \] \[ (0.20)^0 = 1 \] \[ (0.80)^9 \approx 0.134217728 \] Thus, \[ P(X = 0) \approx 1 \cdot 1 \cdot 0.134217728 \approx 0.1342 \] ### Part (b) **Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.** Here, \( k = 1 \): \[ P(X = 1) = \binom{9}{1} (0.20)^1 (0.80)^8 \] Calculating this: \[ \binom{9}{1} = 9 \] \[ (0.20)^1 = 0.20 \] \[ (0.80)^8 \approx 0.16777216 \] Thus, \[ P(X = 1) = 9 \cdot 0.20 \cdot 0.16777216 \approx 9 \cdot 0.033554432 \approx 0.3020 \] ### Part (c) **Find the probability that the number of selected adults saying they were too young is 0 or 1.** This is the sum of the probabilities from parts (a) and (b): \[ P(X = 0 \text{ or } X = 1) = P(X = 0) + P(X = 1) \] Calculating this: \[ P(X = 0 \text{ or } X = 1) = 0.1342 + 0.3020 = 0.4362 \] ### Summary of Results - (a) \( P(X = 0) \approx 0.1342 \) - (b) \( P(X = 1) \approx 0.3020 \) - (c) \( P(X = 0 \text{ or } X = 1) \approx 0.4362 \) Thus, the final answers are: - (a) 0.1342 - (b) 0.3020 - (c) 0.4362