The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. The following table provides a frequency distribution for the number of rooms in U.S. housing units. The frequencies are in thousands.
Rooms __________________________ No. of units
1 ............................................ 601
2 ............................................ 1,404
3 ............................................ 11,433
4 ............................................ 23,636
5 ............................................ 30,440
6 ............................................ 27,779
7 ............................................ 17,868
8+ ........................................... 19,257
Compute the following conditional probabilities directly; that is, do not use the conditional probability rule. For a U.S. housing unit selected at random, determine
a. The probability that the unit has exactly four rooms.
b. The conditional probability that the unit has exactly four rooms, given that it has at least two rooms.
c. The conditional probability that the unit has at most four rooms, given that it has at least two rooms.
d. Interpret your answers in parts (a)-(c) in terms of percentages.