Question

based on a poll, among adults who regret getting tattoos, 14% say that they were too young when they got their tattoos. assume that 10 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 who regrets getting a tattoo says they were too young is $p = 0.14$. So the probability that an adult who regrets getting a tattoo does not say they were too young is $q=1 - p=1 - 0.14 = 0.86$.

Step2: Use the binomial probability formula for $n = 10$ and $k = 0$

The binomial - probability formula is $P(X = k)=C(n,k)\times p^{k}\times q^{n - k}$, where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success on a single trial, $q$ is the probability of failure on a single trial, and $C(n,k)=\frac{n!}{k!(n - k)!}$. Here, $n = 10$, $k = 0$, $p = 0.14$, and $q = 0.86$. Since $C(10,0)=\frac{10!}{0!(10 - 0)!}=1$, then $P(X = 0)=1\times(0.14)^{0}\times(0.86)^{10}$.

Step3: Calculate the result

$(0.14)^{0}=1$, and $(0.86)^{10}\approx0.2213$.

Answer:

$0.2213$