Question

A survey of 200 people included questions about age and whether or not the person had...

A survey of 200 people included questions about age and whether or not the person had any tattoos. The data for these two questions are summarized in the table below. Use the table to answer the questions that follow.

Age # With Tattoo # With No Tattoo Totals by Age
18 to 24 14 48 62
25 to 29 12 29 41
30 to 39 8 13 21
40 to 49 9 22 31
50 to 64 3 22 25
65 and up 1 19 20
Totals 47 153 200

Suppose a person is chosen at random from the 200 people included in this survey. Enter all of your probabilities as percentages, rounded to the nearest tenth of a percent.

a. What is the probability that the person is age 25 to 29 or has a tattoo?

b.  If the randomly selected person has a tattoo, what is the probability that the person is age 25 to 29?

c. If the randomly selected person is age 25 to 29, what is the probability that the person has a tattoo?

Math   Statistics-And-Probability   
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Answer #1

Probability = Favorable Outcomes / Total Outcomes

P(A or B) = P(A) + P(b) - P(A and B)

Also By Bayes Theorem, P(A given B) = P(A And B) / P(B)

_____________________________________________

(a) P(25 - 29 or has a Tattoo)

= P(25 - 29) + P(tattoo) - P(25 - 29 and has a Tattoo)

= 41/200 + 47/200 - 12/200 = 76/200 = 0.380

____________________________________________

(b) P(25 - 29 given he has a tattoo) = P(25 - 29 and has a tattoo) / P(tattoo) = (12/200) / (47/200) = 12/47 = 0.255

______________________________________________

(c) P(Has a tattoo given 25-29 year) = P(has a tattoo and is 25 - 29 years) / P(25-29) = (12/200) / (41/200) = 12/41 = 0.293

______________________________________________

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