Question

Based on a​ poll, among adults who regret getting​ tattoos, ​16% say that they were too young when they got their tattoos. Assume that eight adults who regret getting tattoos are randomly​ selected, and find the indicated probability.

Answer 1

The problem is incomplete, but it is solved using a binomial distribution with
`n = 8` and
`p = 0.16`

Explanation:

For each adult who regret getting tattoos, there are only two possible outcomes. Either they say that they were too young, or they do not say this. The answer of an adult is independent of other adults, 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.

​16% say that they were too young when they got their tattoos.

This means that
`p = 0.16`

Eight adults who regret getting tattoos are randomly​ selected

This means that
`n = 8`

Find the indicated probability.

The binomial distribution is used, with
`p = 0.16, n = 8`, that is:

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

`P(X = x) = C_(8,x).(0.16)^(x).(0.84)^(8-x)`