The City Housing Authority has received 100 applications from qualified applican
ID: 2922093 • Letter: T
Question
The City Housing Authority has received 100 applications from qualified applicants for eight low-income apartments. Three of the apartments are on the north side of town, and five are on the south side. If the apartments are to be assigned by means of a lottery, find the following probabilities.
(a) A specific qualified applicant will be selected for one of these apartments. (Round your answer to three decimal places.)
(b) Two specific qualified applicants will be selected for apartments on the same side of town. (Round your answer to five decimal places.)
Explanation / Answer
(a) The 8 apartments can be assigned to 100 individuals in 100P8 ways = 7503063898176000 ways.
A single applicant can be assigned to 8 apartements. For each assignment, the remaining 99 people can take the 7 houses in 99P7 ways.
=> Probability that a person is assigned one of the apartments = 8 * 99P7 / 100P8
= (8 * 99! * 92!) / (92! 100!)
= 8 / 100
= 0.080.
(b) If the two applicants are assiged to apartments on the north side, they can be assigned in 3P2 = 6 ways.
If the two applicants are assigned to apartements on the south side, they can be assigned in 5P2 = 10 ways.
Altogether, there are 16 ways.
The other 98 people can be assigned to 6 apartments in 98P6 ways.
Probability = 16 * 98P6 / 100P8
= (16 * 98! * 92!) / (100! * 92!)
= 16 / (100 * 99)
= 0.00162.