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# 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

- MathMan TGLv 79 years agoFavorite Answer
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)