Question

The article "Chances are you know someone with a tattoo, and he's not a sailor" included results from a survey of adults aged 18 to 50. The accompanying data are consistent with the summary values given in the article. Assuming these data are representative of adult Americans and that an adult American is selected at random, use the given information to estimate the following probabilities.

(A) P(tattoo)

(B) P(tattoo | age 18-29)

(C) P(tattoo | age 30-50)

(D) P(age 18-29 | tattoo)

At Least One Tattoo No Tattoo
Age 18-29 126 324
Age 30-50 54 396

Answer 1

a) 0.2

b) 0.28

c) 0.12

d) 0.7

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We have the following table:

At Least One Tattoo No Tattoo

Age 18-29 126 324

Age 30-50 54 396

So in total, there are

126 + 324 + 54 + 396 = 900 people

(A) P(tattoo)

This is the probability that a randomly selected person has a tattoo.

Desired outcomes:

126 + 54 = 180

180 people have at least one tattoo

Total outcomes:

There are 900 people.

P(tattoo) = 180/900 = 0.2

(B) P(tattoo | age 18-29)

This the probability that a person aged 18-29 has a tattoo

Desired outcomes:

126 people aged 18-29 have tattoos

Total outcomes:

126 + 324 = 450 people aged 18-29

P(tattoo | age 18-29) = 126/450 = 0.28

(C) P(tattoo | age 30-50)

This the probability that a person aged 30-50 has a tattoo

Desired outcomes:

54 people aged 18-29 have tattoos

Total outcomes:

54 + 396 = 450 people aged 30-50

P(tattoo | age 18-29) = 54/450 = 0.12

(D) P(age 18-29 | tattoo)

The probability that a tattoed person is 18-29.

Desired outcomes:

126 tattoed people are 18-29

Total outcomes

126 + 54 = 180 tattoed people

P(age 18-29 | tattoo) = 126/180 = 0.7