Answer to Question #94994 in Statistics and Probability for likith R

Question

In one Midwestern city, the government has 14 repossessed houses, which are evaluated to be worth about the same. Ten of the houses are on the north side of town and the rest are on the west side. A local contractor submitted a bid to purchase four of the houses. Which houses the contractor will get is subject to a random draw.
a. What is the probability that all four houses selected for the contractor will be on the north side of town?
b. What is the probability that all four houses selected for the contractor will be on the west side of town?
c. What is the probability that half of the houses selected for the contractor will be on the west side and half on the north side of town?

Answer 1

Total number of houses = 14

number of houses on north side = 10

number of houses on west side = 14 - 10 = 4

number of ways of selecting any 4 houses = C(14 ,4)=1001

a.

number of ways of selecting all 4 houses on north side = C(10 ,4) =210

required probability = 210/ 1001 = 30 / 143

b.

number of ways of selecting all 4 houses on west side = C(4 ,4) = 1

required probability = 1/ 1001

c.

number of ways of selecting half of the houses on the west side and half on the north side = C(10 ,2)( C(4 ,2)) =45 (6) = 270

required probability = 270/ 1001