Question

The City Housing Authority has received 75 applications from qualified applicants for nine low-income apartments. Four 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. Two specific qualified applicants will be selected for apartments on the same side of town

Answer 1

Total applications = 75
Apartments on north side of town = 4
Apartments on South side of town = 5

First  person has a 4/75 chance of getting a house in the north side
P(A) = 4/75

And second person has a 3/74 chance of getting a house in the north side
P(B) = 3/74

Probability that 2 qualified applicants will be selected for the north side of town =  P(A∩B) = P(A) x P(B) = (4 ÷ 75) x (3 ÷ 74) = 0.05333 x 0.04054 = 0.00216 

First  person has a 5/75 chance of getting a house in the south side 
P(A) = 5/75

And second person has a 4/74 chance of getting a house in the south side
P(B) = 4/74

Probability that 2 qualified applicants will be selected for the south side of town =  P(A∩B) = P(A) x P(B) = (5 ÷ 75) x (4 ÷ 74) = 0.06666 x 0.05405 = 0.00360