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# PS - probability (easy one)

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Manager
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PS - probability (easy one) [#permalink]

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12 Aug 2007, 15:47
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Question # 22
A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?

(A) 2/27

(B) 1/9

(C) 1/3

(D) 4/27

(E) 2/9
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12 Aug 2007, 16:52
probability of selecting a red ball and then a white ball on 2 successive draws if the ball is returned to the bag after the first draw:

P(red) * P(white)
(3/9) * (2/9) = 6/81 or 2/27

Manager
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13 Aug 2007, 15:49
emarinich wrote:
probability of selecting a red ball and then a white ball on 2 successive draws if the ball is returned to the bag after the first draw:

P(red) * P(white)
(3/9) * (2/9) = 6/81 or 2/27

Oh yeah... That's exactly why I posted this
OA D

[quote]
Actual Answer : D

Explanation
Probability of a desired outcome = Number of favourable outcomes / Total number of possible outcomes.
There are a total of 9 balls in the bag.
3 out of the total 9 balls are red.
Probability of drawing a red ball = 3/9

The one ball that is drawn is returned back into the bag and another ball is drawn.
Now, 2 out of the total 9 balls are white.
Probability of drawing a white ball = 2/9.

Hence probability of drawing a red and a white ball in two successive draws = 3/9 * 2/9 = 1/3 * 2/9 = 2/27.

The order in which the ball is drawn is not specified. It could be a red ball first or it could be a white ball first.
Hence the probability will be 2/27 + 2/27 = 4/27.

Hence (D) is the correct answer.

[end quote]
Manager
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13 Aug 2007, 16:06
The order in which the ball is drawn is not specified. It could be a red ball first or it could be a white ball first.
Hence the probability will be 2/27 + 2/27 = 4/27.

Yes, it is specified. The question said a "red ball and then a white ball"

???
Manager
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13 Aug 2007, 16:08
oops!

I misread - I read a quote of the original question, which was slightly but ever so importantly different from the original - that little word "then" isn't in the question....
13 Aug 2007, 16:08
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# PS - probability (easy one)

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