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

tagged by: vinni.k

### Top Member

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

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.

OA is A

Given: Bowl = only white + only black
Question: P(extracting white ball) = White/(White + Black)

(1) White = 2*Black
P(extracting white ball) = 2*Black/(2*Black + Black) = 2/3
So, s(1) is sufficient.

(2) Here, i am not able to interpret this statement properly.
P(extracting both balls black) = Black/(White + Black) * (Black - 1)/(White + Black - 1) = 0
How to proceed from here ? It is given that the bowl contains only white and only black balls, it means that there are some black balls in the bowl, then how come the probability of extracting both black balls is 0.

Thank you.

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vinni.k 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.
Statement 1:
Of every 3 balls, 1 is black and 2 are white.
Thus, the probability of extracting a white ball = 2/3.
SUFFICIENT.

Statement 2:
Implication:
The bowl contains at most 1 black ball, with the result that it is not possible to extract 2 black balls from the bowl.
Case 1: 1 black ball and 1 white ball
In this case, the probability of extracting a white ball = 1/2.
Case 1: 1 black ball and 2 white balls
In this case, the probability of extracting a white ball = 2/3.
Since the probability can be different values, INSUFFICIENT.

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vinni.k wrote:
Mitch,
Just to confirm my understanding.

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

I am just focusing only on this statement. As you have mentioned that the bowl contains at most 1 black ball. So, we have two cases.
Case 1: for the probability to be 0, the bowl can have 0 black balls.
Case 2: for the probability to be 0, the bowl can have 1 black ball.

If the bowl has more than 1 black ball, then probability will not be 0.

Am i correct ?
Correct!

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Mitch,
Just to confirm my understanding.

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

I am just focusing only on this statement. As you have mentioned that the bowl contains at most 1 black ball. So, we have two cases.
Case 1: for the probability to be 0, the bowl can have 0 black balls.
Case 2: for the probability to be 0, the bowl can have 1 black ball.

If the bowl has more than 1 black ball, then probability will not be 0.

Am i correct ?

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