based on a poll, among adults who regret getting tattoos, 15% say that they were too young when they got…

Explanation:

Step1: Identify the probability of success and number of trials

The probability $p$ that an adult who regrets getting a tattoo says they were too young is $p = 0.15$, and the number of trials $n=9$.

Step2: Use the binomial - probability formula $P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}$, where $C(n,k)=\frac{n!}{k!(n - k)!}$

a. Probability that none of them say they were too young ($k = 0$)

$P(X = 0)=C(9,0)\times(0.15)^{0}\times(1 - 0.15)^{9-0}$ $C(9,0)=\frac{9!}{0!(9 - 0)!}=1$, $(0.15)^{0}=1$, $(1 - 0.15)=0.85$ $P(X = 0)=1\times1\times(0.85)^{9}\approx0.2316$

b. Probability that exactly one says they were too young ($k = 1$)

$P(X = 1)=C(9,1)\times(0.15)^{1}\times(1 - 0.15)^{9 - 1}$ $C(9,1)=\frac{9!}{1!(9 - 1)!}=\frac{9!}{1!8!}=9$ $P(X = 1)=9\times0.15\times(0.85)^{8}\approx0.3679$

c. Probability that the number is 0 or 1

$P(X=0\ or\ X = 1)=P(X = 0)+P(X = 1)$ $P(X=0\ or\ X = 1)\approx0.2316+0.3679 = 0.5995\approx0.5996$

d. To determine if it is unusual

The probability that more than 1 says they were too young is $P(X>1)=1 - P(X\leq1)=1 - 0.5996 = 0.4004>0.05$ So, it is not unusual. The probability that more than 1 of the selected adults say that they were too young is greater than 0.05.

Answer:

a. $0.2316$ b. $0.3679$ c. $0.5996$ d. more than 1; greater than