Question

based on a poll, among adults who regret getting tattoos, 18% say that they were too young when they got their tattoos. assume that six 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. 0.3040 (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. 0.4004 (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: Recall the formula for the probability of a binomial distribution

The formula for the binomial probability 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 in a single trial, and \(C(n,k)=\frac{n!}{k!(n - k)!}\)

Step2: Identify the values for parts (a), (b), and (c)

For this problem, \(n = 6\) (the number of adults selected), \(p=0.18\) (the probability that an adult who regrets getting a tattoo says they were too young), and \(1-p = 0.82\)

Step3: Calculate the probability for part (a)

When \(k = 0\) (none of the adults say they were too young)

$$
LATEXBLOCK0
$$

Step4: Calculate the probability for part (b)

When \(k = 1\) (exactly one adult says they were too young)

$$
LATEXBLOCK1
$$

Step5: Calculate the probability for part (c)

The probability that \(X = 0\) or \(X=1\) is \(P(X=0)+P(X = 1)\)

$$
LATEXBLOCK2
$$

Answer:

\(0.7044\)