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

Answer 1

The probability that both specific qualified applicants will be among the eight selected is given by:
$P(2\ specified)=\frac{2C2\times 48C6}{50C8}=0.0229$
The probability that the two will get apartments on the North side is given by:
$P(North)=\frac{3C2\times5C0}{8C2}=0.107$
The probability that the two will get apartments on the South side is given by:
$P(South)=\frac{5C2\times3C0}{8C2}=0.357$
The events '2 apartments on North side' and '2 apartments on South side' are mutually exclusive. Therefore the probability the two specific qualified applicants will be on the same side of town is 0.107 + 0.357 = 0.464.
Finally, the probability that two specific qualified applicants will be selected for apartments on the same side of town is found from:
$0.0229\times0.464=0.01063$

Answer 2

The solution would be like this for this specific problem:

(3C2 + 5C2)/(50C2) 
= (3 + 10)/1225

= .01061

The probability that two specific qualified applicants will be selected for apartments on the same side of town is 0.0101.

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