If a bowl contains only white and black balls, what is the probability

Question

If a bowl contains only white and black balls, what is the probability of drawing 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 drawn from the bowl without replacement, the probability that both of them will be black is 0.

M16-30

Bunuel · Accepted Answer

Official Solution:

If a bowl contains only white and black balls, what is the probability of drawing a white ball from the bowl? 
 
(1) There are twice as many white balls as black balls in the bowl.
 
White balls make up two-thirds of the total number of balls in the bowl. Therefore, the probability of drawing a white ball is  \frac{2}{3} . Sufficient.
 
(2) If two balls are drawn from the bowl without replacement, the probability that both of them will be black is 0.
 
From this information, we can deduce that the bowl contains only one black ball. However, since we don't know the number of white balls present, we cannot determine the probability of drawing a white ball from the bowl. Not sufficient.

Answer: A

sportyrizwan · Answer

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 ?

rishi2377 · Answer

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.

Dellin · Answer

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

subhashghosh · Answer

The answer is A.

From(1) -> W/B+W = W/(W/2 + W) = 2/3, so sufficient.

From (2), we can only infer that # of Black balls <= 1, but no info about White balls

Yes, we can assume from S2 that there are 0 or 1 black ball. because the probability is 0 can imply three things :

The probablity = B1/N * B2/(N-1)

B1 = # of black balls in container during first draw

B2 = # of black balls during second draw

N = Total # of balls

Because the probability of this even is zero, so:

1) First drawn ball is black but the second is not
2) Second drawn ball is black but the first is not
3) Both the balls are not black.

shinbhu · Answer

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)/t. We don't know the total, so insufficient

A.

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If a bowl contains only white and black balls, what is the probability

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If a bowl contains only white and black balls, what is the probability

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