chacha0212 wrote:A housing subdivision contains only two types of homes: ranch-style homes and townhomes. There are twice as many townhomes as ranch-style homes. There are 3 times as many townhomes with pools than without pools. What is the probability that a home selected at random from the subdivision will be a townhome with a pool?
A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2
This is an EITHER/OR group problem.
Every house is EITHER townhome OR ranch.
Every house EITHER has a pool arts OR does not.
For an EITHER/OR group problem, use a GROUP GRID (also known as a double-matrix) to organize the data.
Let R = ranch, T = townhome, P= pool, NP = no pool.
In the grids below, the entries in any given row or column must add up to the TOTAL of that row or column.
There are 3 times as many townhomes with pools than without pools.
Let the number of townhomes without a pool = 1, implying that the number of townhouses with a pool = 3 and that the total number of townhomes = 1+3 = 4.
The following grid is yielded:
There are twice as many townhomes as ranch-style homes.
Since there are 4 townhomes, the number of ranches = 2.
The following grid is yielded:
What is the probability that a home selected at random from the subdivision will be a townhome with a pool?
According to the resulting grid:
(townhomes with a pool)/total homes) = 3/6 = 1/2.
The correct answer is
E.
I'd rate this as a 500-600 level problem.
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