The City Housing Authority has received 75 applications from qualified applicants for nine low-income apartments. Four of the ap
artments 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
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
