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Ist Part. First piece of information You have 100

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Praetorian
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Ist Part. First piece of information You have 100 [#permalink] New post   15 Oct 2003, 00:09
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Ist Part.

First piece of information

You have 100 large bowls and in each bowl you have 1000 balls.
45 of the large bowls have 700 black balls and 300 red balls.
55 of the large bowls have 300 black balls and 700 red balls.

What is the probability that one randomly selected large bowl have more black balls?

IInd Part

Now from the 100 large bowls, 1 bowl is randomly selected. Then 12 balls
are randomly drawn from the bowl ( with replacement) with the following
results: 8 were black balls and 4 were red balls.

Question 2: What is the probability that this bowl has more black balls?



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Re: Ist Part. First piece of information You have 100 [#permalink] New post   29 Dec 2003, 20:23
For Q1 P = 45/100

for Q2 P = (45/100)* ( 700C8 * 300C4 / 1000C12 )
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Re: Ist Part. First piece of information You have 100 [#permalink] New post   29 Dec 2003, 20:46
The first part is relatively easy but part II throws me off. Can someone explain this in more detail?
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Re: Ist Part. First piece of information You have 100 [#permalink] New post   31 Dec 2003, 10:42
Do not think this is ETS level question.

For second part I would think that the answer would be

= [(45/100) * (700C8 * 300C4 / 1000C12)]/ [{(45/100) * (700C8 * 300C4 / 1000C12)} + {(55/100) * (300C8 * 700C4 / 1000C12)}]

It is basically a conditional probability problem

The required probability = Probability of getting the desired configuration (8 black and 4 red) from a bowl having more black / probability of getting the desired configuration (8 black and 4 red) from ALL the bowls

Praet,

Do you know the answer?
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Re: Ist Part. First piece of information You have 100 [#permalink] New post   31 Dec 2003, 11:09
Yes, I think the answer is good. By the way, for those of you who need to fine tune their probability/combination skills (and want that 700+ score), here is a link and a document giving very good explanations (especially the last 3 problems).

https://www.gmatclub.com/phpbb/viewtopic.php?t=1585

dowload the word document. I clearly understood this complicated problem after reading that document!
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Re: Ist Part. First piece of information You have 100 [#permalink] New post   31 Dec 2003, 12:19
I agree with gmatblast. I hope correct answer will be posted.
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Re: Ist Part. First piece of information You have 100 [#permalink] New post   31 Dec 2003, 13:04
Why?! Why do you leave us to our misery after posting such a beautiful problem? :drunk

(by the way, congrats for becoming CEO) :king



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Re: Ist Part. First piece of information You have 100 [#permalink]
31 Dec 2003, 13:04
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