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Probability problem..Please help


ishti_du

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Dear all

 

I faced a problem in Probability: its like this:

 

A housing subdivision contains only two types of homes:ranch-style homes and townhomes. There are twice as many thownhomes 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 form 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 used my calculation and selected (E = 1/2) as the answer. But the answer sheet says it is (A = 1/6)? :mad:

 

Can anyone help me out here with proper explanation to the answer.

Thanks in advance

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Dear all

 

I faced a problem in Probability: its like this:

 

A housing subdivision contains only two types of homes:ranch-style homes and townhomes. There are twice as many thownhomes 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 form 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 used my calculation and selected (E = 1/2) as the answer. But the answer sheet says it is (A = 1/6)? :mad:

 

Can anyone help me out here with proper explanation to the answer.

Thanks in advance

 

Hi, ishti_du !

 

I have seen this problem before and I've also encountered some difficulties while trying to solve it but I finally succeded.

 

 

The question is about what is the possibility to choose townhome with pools -so let's mark them with Y.

 

It is stated that those type of homes are 3 times as many than those without pools - so we could express the number of the townhomes without pools as (Y/3).

 

The total number of townhomes will be the sum of the two types of townhomes or : Townhomes= Y + (Y/3)=(4/3)Y

 

We know also that the number of the townhomes is twice the number of the ranch-style homes or : Townhomes=2xRanch-style homes

 

Solving this equation for the Ranch-style homes will gives us that: Ranch-style homes=Townhomes/2

 

We can substitute the value of the townhomes:

Ranch-style homes=[(4/3)Y]/2=(4/6)Y

 

Let's see what we have now:

- Townhomes with pools=Y

- Townhomes without pools=(Y/3)

- Total number of townhomes=(4/3)Y

- Ranch-style homes=(4/6)Y

 

To find what is the possibility to select townhome with pools we should calculate the total number of homes or:

- Total number of homes= All townhomes + Ranch-style homes=

=(4/3)Y+(4/6)Y=(12/6)Y

 

Now the final step is to calculate the possibility:

Possibility=(Townhomes with pools)/(Total number of homes)

or

 

Answer=Y/[(12/6)Y]=6/12=1/2

 

Hope this explanation will help you to understand the solution of that problem!

 

Wish you a lot of luck!

Delyan

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Hi, ishtiaque!

Yes, you are completely right - sorry for that stupid blunder :( I have edited my post with the correct answer. Anyway, I think that 1/2 is the right answer but let's wait just a little bit longer to see whether another suggestions will be posted.

Regards,

Delyan

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yeah!! let's see if anyone helps us out here!!

 

Your explanation was great, it helped me a lot....thanks .

 

Hi,ishti_du!

I found the answer explanation for the question in NOVA-GRE book. Here it is:

 

" Since there are twice as many townhomes as ranch-style homes, the probability of selecting a

townhome 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)x(1/4)=(1/6)

The answer is (E).

* Caution: Were you tempted to choose 1/2 for the probability because there are “twice” as many

townhomes? One-half (= 50%) would be the probability if there were an equal number of townhomes and

ranch-style homes. Remember the probability of selecting a townhome is not the ratio of townhomes to

ranch-style homes, but the ratio of townhomes to the total number of homes. To see this more clearly,

suppose there are 3 homes in the subdivision. Then 2 would be townhomes and 1 would be a ranch-style

home. So the ratio of townhomes to total homes would be 2/3. "

 

That's the solution the authors of the problem provided - hope it will clarify how to solve such kind of problems!

 

Regards,

Delyan

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It works great with a number substitution..

 

Assume no.of. ranch style homes = 100.

By problem definition, townhomes = 2* no.of. ranch homes

= 200.

 

Within townhomes, there are townhomes with pool and without pool.

By problem definition,

no of townhomes with pool/ without pool = 3:1

 

Therefore, no of townhomes with pool = 3/4* 200 = 150;

 

Probability of selecting a townhome with a pool = 150/300 = 1/2;

 

1/6 can not be the answer

 

Thanks

Kupps

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