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.)

Explanation:

Step1: Identify the probability of success and failure

The probability that an adult who regrets getting a tattoo says they were too young, $p = 0.15$. So the probability that an adult who regrets getting a tattoo does not say they were too young, $q=1 - p=1 - 0.15 = 0.85$. The number of trials $n = 9$.

Step2: Use the binomial - probability formula

The binomial - probability formula is $P(X = k)=C(n,k)\times p^{k}\times q^{n - k}$, where $C(n,k)=\frac{n!}{k!(n - k)!}$. Here, we want to find the probability that $k = 0$. When $k = 0$, $C(9,0)=\frac{9!}{0!(9 - 0)!}=1$. Then $P(X = 0)=C(9,0)\times(0.15)^{0}\times(0.85)^{9 - 0}$.
Since any non - zero number to the power of 0 is 1, $(0.15)^{0}=1$. So $P(X = 0)=1\times1\times(0.85)^{9}$.

Step3: Calculate the result

$(0.85)^{9}=0.231616946$. Rounding to four decimal places, we get $0.2316$.

Answer:

$0.2316$