The City Housing Authority has received 50 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.

(b) Two specific qualified applicants will be selected for apartments on the same side of town. (Round your answer to five decimal places.)

Question

The City Housing Authority has received 50 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.

(b) Two specific qualified applicants will be selected for apartments on the same side of town. (Round your answer to five decimal places.)

anonymous · Answer

There are 50C2 position pairs for a particular pair of names to be placed in.
3C2 of these position pairs are north selection, 5C2 are south selection, and the others are all non-selection or a mixture of north, south, and non.
So the probability that a particular pair are both north or both south is
(3C2 + 5C2)/(50C2)
= (3 + 10)/1225