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4 September, 01:27

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

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  1. 4 September, 04:08
    0
    a) 0.2

    b) 0.28

    c) 0.12

    d) 0.7

    Step-by-step 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
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