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# A housing subdivision contains only two types of homes:

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Manager
Joined: 19 Aug 2006
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A housing subdivision contains only two types of homes: [#permalink]  07 Sep 2007, 06:37
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A housing subdivision contains only two types of homes: ranch-style homes andtownhomes. There are twice as many townhomes as ranch-style homes. There are 3 timesas many townhomes with pools than without pools. What is the probability that a homeselected 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
Director
Joined: 22 Aug 2007
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Re: PS-Probability [#permalink]  07 Sep 2007, 07:03
johnycute wrote:
A housing subdivision contains only two types of homes: ranch-style homes andtownhomes. There are twice as many townhomes as ranch-style homes. There are 3 timesas many townhomes with pools than without pools. What is the probability that a homeselected 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

I got E,

R is # of ranchhomes
T is # of townhomes

"There are twice as many townhomes as ranch-style homes." translates T=2R. Then total number of houses is 3R
"There are 3 timesas many townhomes with pools than without pools. " translates the ratio of "with pools to without pools" is 3:1. Or 75% {3/4} of T with pools and 1/4 {25%} of T without pools. Then # of houses with pools is 0,75*T or 0,75*2R.

"What is the probability that a homeselected at random from the subdivision will be a townhome with a pool?" translates
# of houses with pools/ total # of houses=?

0,75*2R/3R = 1/2

Please, let know if I missed something.
Director
Joined: 03 May 2007
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Schools: University of Chicago, Wharton School
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Re: PS-Probability [#permalink]  07 Sep 2007, 07:18
johnycute wrote:
A housing subdivision contains only two types of homes: ranch-style homes andtownhomes. There are twice as many townhomes as ranch-style homes. There are 3 timesas many townhomes with pools than without pools. What is the probability that a homeselected 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

E.

R = x
T = 2x
total = 3x

T (No Pool) = 2x/4
T (Pool) = 2x - 2x/4 = 6x/4

P9Pool) = (6x/4)/3x = 1/2
VP
Joined: 08 Jun 2005
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Just plug in numbers !

Total homes = 90

ranch-style = 30

town-homes = 60

town-homes with pool = 45

town-homes without a pool = 15

probability that a homeselected at random from the subdivision will be a townhome with a pool = 45/90 = 1/2

Senior Manager
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The same answer, agree with all

Ans: E
Manager
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Re: PS-Probability [#permalink]  07 Sep 2007, 11:15
johnycute wrote:
A housing subdivision contains only two types of homes: ranch-style homes andtownhomes. There are twice as many townhomes as ranch-style homes. There are 3 timesas many townhomes with pools than without pools. What is the probability that a homeselected 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

I got E too. Basically, 2/3 houses are Townhouses among the total houses. Out of those 2/3 houses, ONLY 3/4 or 75% are townhouses with pools i.e.

3/4 * 2/3 = 1/2 (E)
Manager
Joined: 19 Aug 2006
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I also got the answer 1/2, but in some book the OE is:

Since there are twice as many townhomes as ranch-style homes, the probability of selecting atownhome is 2/3.* Now, “there are 3 times as many townhomes with pools than without pools.”So the probability that a townhome will have a pool is 3/4. Hence, the probability of selecting a
townhome with a pool is

2/3 * 1/4 = 1/6

Is it correct?
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