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# A bowl contains white and black balls. What is the

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SVP
Joined: 21 Jan 2007
Posts: 1856
Location: New York City
A bowl contains white and black balls. What is the  [#permalink]

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Updated on: 26 Jul 2014, 08:21
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70% (01:10) correct 30% (00:59) wrong based on 297 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

M16-30

Originally posted by bmwhype2 on 06 Nov 2007, 08:33.
Last edited by Bunuel on 26 Jul 2014, 08:21, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Intern
Joined: 01 Nov 2007
Posts: 49
Re: A bowl contains white and black balls. What is the  [#permalink]

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06 Nov 2007, 08:59
1
I will go with A

1. Since there are twice as many white balls as black balls.
Probability to extract a white ball will be 2/3

2. "If two balls are extracted from the bowl, the probability that both of them are black is 0"
This is only possible when either there is no black ball or either 1 black ball. So we cannot determine the probability of extracting a white ball...

Am I correct ?
Manager
Joined: 18 Jun 2007
Posts: 180
Re: A bowl contains white and black balls. What is the  [#permalink]

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06 Nov 2007, 09:09
2
1
sportyrizwan wrote:
I will go with A

1. Since there are twice as many white balls as black balls.
Probability to extract a white ball will be 2/3

2. "If two balls are extracted from the bowl, the probability that both of them are black is 0"
This is only possible when either there is no black ball or either 1 black ball. So we cannot determine the probability of extracting a white ball...

Am I correct ?

Yup sporty. Just one clearification.

I assume that sufficiency of A is pretty clear.

As far as B is concern, black ball cant not be 0 since question states that
A bowl contains white and black balls

So it is clear that there is 1 black ball.
Why B is insufficient?

assume there are only 1 black and 1 white ball- probability to extract a white ball from the bowl= 1/2

Now assume there are 3 white balls and 1 black ball - probability to extract a white ball from the bowl is 3/4

B is insufficient. Answer is A.
Intern
Joined: 04 Jan 2008
Posts: 47
Re: A bowl contains white and black balls. What is the  [#permalink]

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08 Jan 2008, 10:31
1
A
S1 gives 2/3- suffi
S2 gives, prob both black=0, which says that there is only one black ball in there. So, the no of white balls can be anything, so we cant find prob of white= s2 not suffi
VP
Joined: 07 Nov 2007
Posts: 1060
Location: New York
Re: A bowl contains white and black balls. What is the  [#permalink]

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26 Aug 2008, 12:00
bmwhype2 wrote:
A bowl contains white and black balls.
What is the probability to extract a white ball from the bowl?

1. There are twice as many white balls as black balls
2. If two balls are extracted from the bowl, the probability that both of them are black is 0

A

State 1 :
W:B= 2n:n

p= 2nC1/3nC1 = 2/3

state 2:
two possibilities that all are WHITE balls OR one Black ball and others are White.
insuffcieint
Manager
Joined: 27 Oct 2008
Posts: 125
Re: A bowl contains white and black balls. What is the  [#permalink]

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28 Sep 2009, 10:07
A bowl contains white and black balls.
What is the probability to extract a white ball from the bowl?

1. There are twice as many white balls as black balls
2. If two balls are extracted from the bowl, the probability that both of them are black is 0

Soln.

Statement 1 alone is sufficient.
Assuming that there are x black balls. Hence 2x white balls.
Thus probability of drawing a white ball is = 2x/3x = 2/3

Statement 2 alone is not sufficient.
From this statement we cannot guess the number of white and black balls present.
Manager
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Location: Ghana
Concentration: Finance, Finance
Schools: Cambridge
GMAT 1: 690 Q47 V37
GPA: 3.9
WE: Accounting (Education)
Re: A bowl contains white and black balls. What is the  [#permalink]

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29 Nov 2011, 04:19
Going with A. Statement two says nothg about the number of white balls
Manager
Joined: 12 Oct 2011
Posts: 137
Re: A bowl contains white and black balls. What is the  [#permalink]

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04 Jan 2012, 11:54
Clearly A. Statement 1 gives us the probability as 2/3 and statement 2 does not gives us any information regarding the number of white balls or the total number of balls.
Manager
Joined: 29 Jul 2011
Posts: 69
Location: United States
Re: A bowl contains white and black balls. What is the  [#permalink]

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04 Jan 2012, 12:25
1
The stem can be rephrased as w/(w+b)?

1. w = 2b. Sufficient by substitution
2. This means that there is only one black ball. Let t = total, so black = 1 and white = t - 1. This implies (t-1)/[(t-1)+1] = (t-1)/t. We don't know the total, so insufficient

A.
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Re: A bowl contains white and black balls. What is the  [#permalink]

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01 Aug 2020, 04:57
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Re: A bowl contains white and black balls. What is the   [#permalink] 01 Aug 2020, 04:57