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 summary values given in the article. At Least One Tattoo No Tattoo Age 18–29 190 310 Age 30–50 60 440 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)

Answer 1

Explanation:

Hello!

People aged 18 to 50 were asked if they had at least one tattoo (Yes, No), the results of the survey were arranged according to the age intervals [18;29]; [30;50]

At least one tattoo ; No tattoo ; Total

[18;29] ; 190 ; 310 ; 500

[30;50] ; 60 ; 440 ; 500

Total ; 250 ; 750 ; 1000

After you arranged the information in a contingency table it is more simple to calculate the asked categories. To calculate the probability values for each category you have to divide the total observations of the given category by the total of the sample.

a. P(Tattoo)

To calculate the probability of the surveyed adults that have at least one tattoo you have to divide the total of people that answered "yes", the number corresponding to this category is on the margins of the table, by the total of adults that where surveyed:

P(Tattoo)= 250/1000= 0.25

b. P(Tattoo ∩ age 18-29)

To calculate this probability you have to use the total of observation of people that have at least one tattoo and are aged 18-29, this number is in the body of the table, by the total of people surveyed.

P(Tattoo ∩ age 18-29)= 190/1000= 0.19

c. P(Tattoo ∩ age 30-50)

Same as before, the value of the probability is the total of observation of people that have a tattoo and are aged 30-50, this number is in the body of the table, by the total of people surveyed.

P(Tattoo ∩ age 30-50)= 60/1000= 0.06

d. P(age 18-29)

To calculate this probability you have to use the value in one of the margins of the table, corresponding to the total of people surveyed aged 18-29 by the total of people surveyed.

P(age 18-29)= 500/1000= 0.5

I hope it helps!

Answer 2

a) 0.25

b) 0.38

c) 0.12

d) 0.64

Explanation:

We have these following informations.

There are 500 people between 18 and 29. Of those 190 have at least one tattoo and 310 have no tattoo.

There are also 500 people between 30 and 50. Of those, 60 have at least one tattoo and 440 have no tattoo.

a) P(tattoo)

There are 1000 people. Of those, 190+60 = 250 have tattoo. So P(tattoo) = 250/1000 = 0.25.

b) P(tattoo|age 18-29)

There are 500 people aged 18-29. Of those, 190 have at least one tattoo. So P(tattoo|age 18-29) = 190/500 = 0.38.

c) P(tattoo|age 30-50)

There are 500 people aged 18-29. Of those, 60 have at least one tattoo. So P(tattoo|age 30-50) = 60/500 = 0.12.

d) P(age 18-29|tattoo)

250 people have at least one tattoo. Of those, 160 are between 18 and 29. So P(age 18-29|tattoo) = 160/250 = 0.64.