Problem

Based on a poll, among adults who regret getting tattoos, $18 \%$ say that they were too young when they got their tattoos. Assume that four 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.)

Solution

Step 1 :This problem is a binomial probability problem. We have four trials (four adults who regret getting tattoos), and we want to find the probability that none of them say that they were too young when they got their tattoos. The probability of success (an adult saying they were too young) is $18 \%$ or $0.18$. The probability of failure (an adult not saying they were too young) is $1 - 0.18 = 0.82$.

Step 2 :The formula for binomial probability is: \[P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\] where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success, and $C(n, k)$ is the combination of $n$ items taken $k$ at a time.

Step 3 :In this case, we want $k=0$, so the formula simplifies to: \[P(X=0) = (1-p)^n\]

Step 4 :Substituting the given values into the formula, we get: \[P(X=0) = (1-0.18)^4 = 0.4521\]

Step 5 :Final Answer: The probability that none of the selected adults say that they were too young when they got their tattoos is approximately \(\boxed{0.4521}\).

From Solvely APP
Source: https://solvelyapp.com/problems/19335/

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