The article Chances Are You Know Someone with a Tattoo and H

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 summary values given in the article shown below. Assuming these data are representative of adults in the United States and that a U.S. adult is selected at random, use the given information to estimate the following probabilities.

At Least One Tattoo No Tattoo
Age 18Â29 70 180
Age 30Â50 30 220

(a) P(tattoo)


(b) P(tattoo | age 18Â29)


(c) P(tattoo | age 30Â50)


(d) P(age 18Â29 | tattoo)

Solution

Given,

a. P(tattoo) = n(At least 1 Tatto) / Total = 100/500 = 0.2

b. P(tattoo | age 18-29) = n(At least 1 Tatto in age 18-29) / Total in age 18-29 = 70/250 = 0.28

c. P(tattoo | age 30-50) = n(At least 1 Tatto in age 30-50) / Total in age 30-50 = 30/250 = 0.12

d. P(age 18-29 | tattoo) = n(At least 1 Tatto in age 18-29) / Total in at least 1 tattoo = 70/100 = 0.7