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. \( \square \) (Round to four decimal places as needed.)

To find the probability that none of the selected adults say that they were too young to get tattoos, we can use the binomial probability formula. Let: - \( n = 9 \) (the number of adults selected) - \( p = 0.20 \) (the probability that an adult regrets getting a tattoo because they were too young) - \( q = 1 - p = 0.80 \) (the probability that an adult does not regret getting a tattoo for that reason) We want to find the probability that none of the 9 adults say they were too young, which means we want to find \( P(X = 0) \), where \( X \) is the number of adults who say they were too young. The probability mass function for a binomial distribution is given by: \[ P(X = k) = \binom{n}{k} p^k q^{n-k} \] For \( k = 0 \): \[ P(X = 0) = \binom{9}{0} (0.20)^0 (0.80)^{9} \] Calculating this step-by-step: 1. Calculate \( \binom{9}{0} \): \[ \binom{9}{0} = 1 \] 2. Calculate \( (0.20)^0 \): \[ (0.20)^0 = 1 \] 3. Calculate \( (0.80)^{9} \): \[ (0.80)^{9} \approx 0.134217728 \] Putting it all together: \[ P(X = 0) = 1 \cdot 1 \cdot (0.80)^{9} \approx 0.1342 \] Thus, the probability that none of the selected adults say that they were too young to get tattoos is approximately: \[ \boxed{0.1342} \]