Question

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	44	57
45-64	35	40
65 and over	21	63

(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?

Answer 1

Solution(a)
Total number of adults = 44+35+21+57+40+63 = 260
We need to calculate the probability that an adult selected at random from this population is a renter which can be calculated as
P(Renter) = Total number of adults in who are renters / Total Number of adults = (57+40+63)/257 = 160/260 = 0.6154
So there is a 61.54% probability that an adult selected at random from this population is a renter.
Solution(b)
Here we need to calculate the probability that he or she is in the 21-44 age bracket if a renter is selected so we will use conditional probability which can be calculated as
P(21-44 age bracket | Renter)= P(21 - 44 Age bracket and Renter)/ P(Renter) = (Total number of adults in 21-44 age bracket and Renter/ Total number of adults)/(Total number of renter/Total number of adults)= (57/260)/((57+40+63)/260) = 57/160 = 0.3563
So there is a 35.63% probability that he or she is in the 21-44 age bracket If a renter is selected at random.
Solution(c)
Here we need to calculate the probability that he or she is in 45 years old or older age bracket if a renter is selected so we will use conditional probability which can be calculated as
P(45 old and older age bracket | Renter)= P(45 old and older age bracket and Renter)/ P(Renter) = (Total number of adults in 45 old and older age bracket and Renter/ Total number of adults)/(Total number of renter/Total number of adults)= ((40+63)/260)/((58+42+57)/260) = 103/160 = 0.6437
So there is a 64.37% probability that he or she is in the 45 old or older age bracket If a renter is selected at random.