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M16-30

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Bunuel
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M16-30 [#permalink] New post   16 Sep 2014, 00:59
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66% (01:12) correct 34% (01:11) wrong based on 196 sessions
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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.
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Bunuel
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Re: M16-30 [#permalink] New post   14 Jun 2017, 05:45
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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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Re M16-30 [#permalink] New post   16 Sep 2014, 00:59
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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.


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disharupani
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Re: M16-30 [#permalink] New post   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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Bunuel
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Re: M16-30 [#permalink] New post   03 May 2023, 08:26
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re M16-30 [#permalink] New post   12 Aug 2023, 02:08
I think this is a high-quality question and I agree with explanation.
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Re M16-30 [#permalink]
12 Aug 2023, 02:08
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