Question

based on a poll, among adults who regret getting tattoos, 18% 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: Identify the binomial probability formula

The binomial probability formula is \(P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}\), where \(n\) is the number of trials, \(k\) is the number of successes, \(p\) is the probability of success in a single trial, and \(C(n,k)=\frac{n!}{k!(n - k)!}\)

Here, \(n = 6\) (the number of adults selected), \(k = 0\) (the number of adults who say they were too young), \(p=0.18\) (probability that an adult says they were too young)

Step2: Calculate \(C(n,k)\)

\(C(6,0)=\frac{6!}{0!(6 - 0)!}=\frac{6!}{6!×1}=1\)

Step3: Calculate \((1 - p)^{n - k}\)

\(1-p = 1 - 0.18=0.82\), \(n - k=6-0 = 6\)
\((1 - p)^{n - k}=(0.82)^{6}\)
\((0.82)^{6}=0.82\times0.82\times0.82\times0.82\times0.82\times0.82\approx0.304\)

Step4: Calculate \(P(X = 0)\)

\(P(X = 0)=C(6,0)\times(0.18)^{0}\times(0.82)^{6}\)
Since \((0.18)^{0}=1\)
\(P(X = 0)=1\times1\times0.304=0.304\)

Answer:

\(0.3040\)