Question

based on a poll, among adults who regret getting tattoos, 15% 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.
(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.
(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.
(round to four decimal places as needed.)

Explanation:

Step1: Identify probability formula

This is a binomial - probability problem. 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 on a single - trial, and $C(n,k)=\frac{n!}{k!(n - k)!}$. Here, $n = 9$ (number of adults selected), $p=0.15$ (probability that an adult says they were too young to get tattoos), and $1 - p = 0.85$.

Step2: Calculate probability for part a ($k = 0$)

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

Step3: Calculate probability for part b ($k = 1$)

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

Step4: Calculate probability for part c

$P(X = 0\text{ or }X = 1)=P(X = 0)+P(X = 1)$. Substitute the values from part a and part b: $P(X = 0\text{ or }X = 1)\approx0.2316+0.3679 = 0.5995$.

Answer:

a. $0.2316$
b. $0.3679$
c. $0.5995$