Probability of Pulling out a blue marble exactly 3 times

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A jar contains marbles of several different colors. Some marbles are to be taken from the jar one at a time, examined and the put back in the jar. What is the probability that exactly three of next five marbles taken from the jar will be blue?

(1) The probability that all of the next five marbles taken from the jar are blue is 243/3125.

(2) The probability that none of the next five marbles taken from the jar are blue is 32/3125.

Statement 2 gives me the prob of one single marble NOT being blue. How can statement 2 help me calculating the prob of marble BEING blue? There are seven colors, so am not sure if I can apply 1-2/5 logic here.

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by GMATGuruNY » Sun Dec 22, 2013 9:23 am
Mustcrackgmat wrote:A jar contains marbles of several different colors. Some marbles are to be taken from the jar one at a time, examined and the put back in the jar. What is the probability that exactly three of next five marbles taken from the jar will be blue?

(1) The probability that all of the next five marbles taken from the jar are blue is 243/3125.

(2) The probability that none of the next five marbles taken from the jar are blue is 32/3125.

Statement 2 gives me the prob of one single marble NOT being blue. How can statement 2 help me calculating the prob of marble BEING blue? There are seven colors, so am not sure if I can apply 1-2/5 logic here.
P(blue) + P(not blue) = 1.
Let P(blue) = x/y and P(not blue) = a/b.
Thus:
x/y + a/b = 1.

Statement 1: The probability that all of the next five marbles taken from the jar are blue is 243/3125.
Since P(blue) = x/y, we get:
(x/y) * (x/y) * (x/y) * (x/y) * (x/y) = 243/3125
(x/y)� = 243/3125
x/y = 3/5.
Since we know that P(blue) = x/y = 3/5, we can determine the probability that exactly three of the next five marbles taken from the jar will be blue.
SUFFICIENT.

Statement 2: The probability that none of the next five marbles taken from the jar are blue is 32/3125.
Since P(not blue) = a/b, we get:
(a/b) * (a/b) * (a/b) * (a/b) * (a/b) = 32/3125
(a/b)� = 32/3125
a/b = 2/5.
Since x/y + a/b = 1, we get:
x/y = 1 - a/b = 1 - 2/5 = 3/5.
Since we know that P(blue) = x/y = 3/5, we can determine the probability that exactly three of the next five marbles taken from the jar will be blue.
SUFFICIENT.

The correct answer is D.
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by dominhtri1995 » Sun Dec 22, 2013 10:06 am
Hi GuruNY

I have a question. How can you know that the probability will not change after a marble is taken out ?


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by AbhiJ » Sun Dec 22, 2013 10:43 am
because you are replacing marbles.

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by Mustcrackgmat » Mon Dec 23, 2013 8:18 am
Hi GuruNY

With the help of statement 2, I can find the prob of pulling put at least one blue marble. How does this help me find the prob of pulling out exactly 3? I can pull out at least 3 marbles or maybe more? I am not clear on this?