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 ten 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
0.2213 (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
0.3603 (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 relevant probabilities

Let $p = 0.14$ be the probability that an adult who regrets getting a tattoo says they were too young, so $q=1 - p=1 - 0.14 = 0.86$. We use the binomial - probability formula $P(X = k)=C(n,k)\times p^{k}\times q^{n - k}$, where $n = 10$ is the number of trials, $k$ is the number of successes, and $C(n,k)=\frac{n!}{k!(n - k)!}$.

Step2: Recall results from parts (a) and (b)

From part (a), $P(X = 0)=0.2213$. From part (b), $P(X = 1)=0.3603$.

Step3: Calculate $P(X = 0\ or\ X = 1)$

Since the events $X = 0$ and $X = 1$ are mutually - exclusive, we use the addition rule for mutually - exclusive events $P(A\ or\ B)=P(A)+P(B)$. So $P(X = 0\ or\ X = 1)=P(X = 0)+P(X = 1)$.
$P(X = 0)+P(X = 1)=0.2213 + 0.3603=0.5816$

Answer:

$0.5816$