Question

Based on a​ poll, among adults who regret getting​ tattoos, 27​% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly​ selected, and find the indicated probability. a. Find the probability that none of the selected adults say that they were too young to get tattoos.

Answer 1

0.2073 = 20.73% probability that none of the selected adults say that they were too young to get tattoos.

Explanation:

For each adult, there are only two possible outcomes. Either they say they were too young to get tattoos, or they do not say it. The probability of an adult saying this is independent of any other adult, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

27​% say that they were too young when they got their tattoos.

This means that
`p = 0.27`

Assume that five adults who regret getting tattoos are randomly​ selected

This means that
`n = 5`

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

This is
`P(X = 0)`. So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 0) = C_(5,0).(0.27)^(0).(0.73)^(5) = 0.2073`

0.2073 = 20.73% probability that none of the selected adults say that they were too young to get tattoos.