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# A housing subdivision contains only two types of homes:

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A housing subdivision contains only two types of homes: [#permalink]

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03 Jul 2005, 11:07
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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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03 Jul 2005, 12:55
AJB77 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

town w/o pools - n
town w/ pools - 3n
ranch - 2n

prob(t w/ pool) = 3n/(6n) = 1/2 or E
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13 Jul 2005, 05:33
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

Consider there are 60 homes in the town.

Thus, there are 20 ranch homes and 40 town homes.

Also, within 40 ranch homes, 30 have pool, 10 do not.

So, the probabilty of picking up a townhome = 40/60= 2/3
the probability of picking up a pool in the townhomes= 30/ 40 = 3/4

Hence the probability of a townhome with a pool = 2/3*3/4= 1/2

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16 Jul 2005, 21:50
sa_samie wrote:
Consider there are 60 homes in the town.

Thus, there are 20 ranch homes and 40 town homes.

Also, within 40 ranch homes, 30 have pool, 10 do not.

So, the probabilty of picking up a townhome = 40/60= 2/3
the probability of picking up a pool in the townhomes= 30/ 40 = 3/4

Hence the probability of a townhome with a pool = 2/3*3/4= 1/2

Samie, I like the way you solved this problem - it was very similar to my method. Except I think you did too much work. You used a combination of two methods, instead of one, which calls for twice as much work. I did the same as you, by picking a number of total houses and plugging that number in to arrive at 60 total homes: 20 ranch homes, 30 townhomes with pool, 10 townhomes without pool. But I disagree with your next step. The shortest method from this point is to immediately take the ratio of homes you are looking for, instead of going back to using some math formula. Since you are looking for townhomes with a pool, simply take that number (30) over the total (60) = 30/60 = 1/2. This would have saved you the step of going back to multiplication. In fact if you are going to do the multiplication step:

Hence the probability of a townhome with a pool = 2/3*3/4= 1/2

Then there is no point plugging in the number 60 in the formula. Its best to choose one way or the other.
16 Jul 2005, 21:50
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