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# M16-30

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:59
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Difficulty:

35% (medium)

Question Stats:

64% (00:53) correct 36% (00:47) wrong based on 151 sessions

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If a bowl contains only white and black balls, what is the probability of extracting a white ball from the bowl?

(1) There are twice as many white balls as black balls in the bowl

(2) If two balls are extracted from the bowl, the probability that both of them will be black is 0

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16 Sep 2014, 00:59
Official Solution:

Statement (1) by itself is sufficient. White balls account for two thirds of the total number of balls in the bowl. Hence, the probability of extracting a white ball is $$\frac{2}{3}$$.

Statement (2) by itself is insufficient. From S2 it follows that the bowl contains only one black ball. But because we don't know how many white balls there are, we cannot answer the question.

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11 Aug 2015, 01:54
I think this is a poor-quality question and I don't agree with the explanation. The solution doesn't hold because the number of black balls and white balls could be equal to zero.
Hence the first statement is insufficient: if W=0 and B=0 then W=2B=0 and P(W)=0
Alternatively: if W=2 and B=1 then W=2B=2 and P(W)=2/3
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12 Aug 2015, 10:33
1
Carnivor646 wrote:
I think this is a poor-quality question and I don't agree with the explanation. The solution doesn't hold because the number of black balls and white balls could be equal to zero.
Hence the first statement is insufficient: if W=0 and B=0 then W=2B=0 and P(W)=0
Alternatively: if W=2 and B=1 then W=2B=2 and P(W)=2/3

Because the question says "If a bowl contains only white and black balls", I think that you can reject the hypothesis of zero balls in the bowl.
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07 Jul 2016, 20:17
Bunuel wrote:
If a bowl contains only white and black balls, what is the probability of extracting a white ball from the bowl?

(1) There are twice as many white balls as black balls in the bowl

(2) If two balls are extracted from the bowl, the probability that both of them will be black is 0

Can someone elaborate Statement 2 pls..how we got b=1

i got b=1 or b=0
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08 Jul 2016, 07:14
1
smartguy595 wrote:
Bunuel wrote:
If a bowl contains only white and black balls, what is the probability of extracting a white ball from the bowl?

(1) There are twice as many white balls as black balls in the bowl

(2) If two balls are extracted from the bowl, the probability that both of them will be black is 0

Can someone elaborate Statement 2 pls..how we got b=1

i got b=1 or b=0

I understand how you got b=0 there but we are told that a bowl contains only white and black balls, which means that the number of white and black balls is more than 0.

Hope it's clear.
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20 Jul 2016, 12:12
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. How can it be derived per S(2) that there was only one black ball? It may well be the case there was more than 1 black ball however none were picked in the first two attempts.
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20 Jul 2016, 12:17
1
njj1984 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. How can it be derived per S(2) that there was only one black ball? It may well be the case there was more than 1 black ball however none were picked in the first two attempts.

The second statement talks about the probability of picking 2 black balls, which is said to be 0. So there cannot be 2 or more black balls.
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22 May 2017, 08:12

I am not understand this question !

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13 Jun 2017, 10:02
I would like to compare this question with the following question:

M09-11
A bowl contains green and blue chips only. If two chips are drawn from the bowl (without replacement) what is the probability that both chips will be blue?
(1) The ratio of blue chips to green chips is 3:4.
(2) There are 5 more green chips than blue chips.

Here statement (1) gives information - ratio of green chips:blue chips = 3:4, - this statement is not sufficient to answer
compare it to statement (1) of above mentioned question ratio of white balls:black balls = 2:1 - but this statement is sufficient to answer

Why so?
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14 Jun 2017, 05:45
2
disharupani wrote:
I would like to compare this question with the following question:

M09-11
A bowl contains green and blue chips only. If two chips are drawn from the bowl (without replacement) what is the probability that both chips will be blue?
(1) The ratio of blue chips to green chips is 3:4.
(2) There are 5 more green chips than blue chips.

Here statement (1) gives information - ratio of green chips:blue chips = 3:4, - this statement is not sufficient to answer
compare it to statement (1) of above mentioned question ratio of white balls:black balls = 2:1 - but this statement is sufficient to answer

Why so?

Because in one case we are choosing 1 item and in another 2 items.

For example, if the ratio of blue chips to green chips is 3:4, then the probability of choosing a blue chip will be 3/7, not matter how many chips are there: 7, 14, 21, 28, ... But the probability of choosing 2 blue chips will depend on the total number of chips. If the total number is 7, then P(bb) = 3/7*2/6 but if the total number is 14, then P(bb) = 6/14*5/13.

Hope it's clear.
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16 Jun 2017, 02:49
Thanks.... It's clear now

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04 Jul 2017, 23:47
Bunuel wrote:
smartguy595 wrote:
Bunuel wrote:
If a bowl contains only white and black balls, what is the probability of extracting a white ball from the bowl?

(1) There are twice as many white balls as black balls in the bowl

(2) If two balls are extracted from the bowl, the probability that both of them will be black is 0

Can someone elaborate Statement 2 pls..how we got b=1

i got b=1 or b=0

I understand how you got b=0 there but we are told that a bowl contains only white and black balls, which means that the number of white and black balls is more than 0.

Hope it's clear.

It could have been 2 black balls to begin with, and after x-2 black balls it will equal zero. Isn't it?
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04 Jul 2017, 23:53
pg1 wrote:

It could have been 2 black balls to begin with, and after x-2 black balls it will equal zero. Isn't it?

Not sure what you are trying to say but the second statement talks about the probability of picking 2 black balls, which is said to be 0. So there cannot be 2 or more black balls.
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Re: M16-30   [#permalink] 04 Jul 2017, 23:53
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# M16-30

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