Bayes Theorem math problem help?

A study conducted by the Metro Housing Agency in a midwestern city revealed the following information concerning the age distribution of renters within the city. (Round your answers to four decimal places.)

Age Adult Population, % Group Who Are Renters, %

21-44 (50) (55)

45-64 (27) (41)

65 and over (23) (59)

(a) What is the probability that an adult selected at random from this population is a renter?

(b) If a renter is selected at random, what is the probability that he or she is in the 21-44 age bracket?

(c) If a renter is selected at random, what is the probability that he or she is 45 years old or older?

1 Answer

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  • 9 years ago
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    We must weight the proportion of renters in each group

    by the percentage the group represents of the whole population.

    Suppose there are 1000 people overall in population.

    Age

    % of pop ... Age ... renter ... non-renter

    50 ..... . .... 21-44 .. 275 ... 225 ..... [ 500 total divided 55-45]

    27 ..... . .... 45-64 .. 110.7 . 159.3 ..[ 270 total divided 41-59]

    23 ..... . .... 65-99 .. 135.7 . 94.3 ... [ 230 total divided 59-41]

    100 .......... Totals: . 521.4 .. 478.6 [ 1000 ]

    a) P(renter) = 521.4 / 1000 = 52.14 %

    b) P(21-44 | renter) = 275 / 521.4 = 52.74%

    c) P(45+ | renter) = complement of previous = 47.26% (or 246.4 / 521.4)

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