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Probability question

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by aratister » Wed Dec 14, 2011 5:36 pm
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
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by pemdas » Wed Dec 14, 2011 6:10 pm
2t:1r
3tp:1wp
P(tp)=2/3 * 3/4 = 1/2
e
aratister 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
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by Anurag@Gurome » Wed Dec 14, 2011 7:52 pm
aratister 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
Let there are 3 homes in the subdivision. Then 2 will be town homes and 1 will be ranch-style home.
So, probability of selecting a town home = 2/3.
Since, there are 3 times as many townhomes with pools than without pools so probability that a town home will have a pool is 3/4.

Hence, required probability = 2/3 * 3/4 = [spoiler]1/2[/spoiler]

The correct answer is E.
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by ankush123251 » Wed Dec 14, 2011 11:35 pm
Let there be 9 homes in all....
Then # of townhomes = 2/3 * 9 = 6 and # of ranch style = 3.
Again # of townhomes with pool = 3/4 * 6 = 4.5(Dont worry about this not bein an integer,you are gonna take ratio only later).
therefore Probabilty = 4.5/9 =1/2.
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by LalaB » Thu Dec 15, 2011 7:58 am
T=2*R
Tp=3*Tnp

let Tnp=1, then Tp=3 T=Tp+Tnp=4 and 4=2R R=2

so, in total we have-

Tnp -Tp- Tp- Tp- R -R total=6

Tp/total=3/6=1/2
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