M16-30

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.

Bunuel · 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

disharupani · Answer

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?

Bunuel · Answer

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.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

ruis · Answer

I dont understand why we can infer from statement 2 that the number of black ball is one. Can you please help me?

Bunuel · Answer

If there were two or more black balls, the probability would be more than 0. The probability being 0 implies there is no chance of picking two black balls, indicating there are fewer than two black balls. Since we know there is at least one, there must be exactly one black ball.

Bhavita. · Answer

@Bunnel in the second part how can we say there is at least one black ball from the given statement

bowl contains only white and black balls (can we not consider that there can be a scenario of all white balls)

Bunuel · Answer

The phrase "a bowl contains only white and black balls" implies that there is at least one ball of each color. It rules out the possibility of having all white balls.

sssdd1234 · Answer

I think this is a  high-quality  question and I agree with explanation.

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M16-30

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