Question

based on a poll, among adults who regret getting tattoos, 21% say that they were too young when they got their tattoos. assume that six 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.)

Explanation:

Step1: Determine the probability of an adult not saying they were too young

The probability that an adult says they were too young is \(p = 0.21\). So the probability that an adult does not say they were too young is \(q=1 - p=1 - 0.21 = 0.79\)

Step2: Use the multiplication rule for independent events

Since we are selecting \(n = 6\) adults and we want the probability that none of them say they were too young. For independent events \(A_1,A_2,\cdots,A_6\) (where \(A_i\) is the event that the \(i -\)th adult does not say they were too young), the probability \(P(A_1\cap A_2\cap\cdots\cap A_6)\) is given by \(q\times q\times\cdots\times q\) (6 times). Using the formula \(P=(q)^n\), with \(n = 6\) and \(q = 0.79\)

$$P=(0.79)^6$$

$$P=0.79\times0.79\times0.79\times0.79\times0.79\times0.79$$

$$P\approx0.2503$$

Answer:

\(0.2503\)