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Probability Again

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by sampath » Sun May 22, 2011 11:00 pm
If two balls are randomly drawn from a green urn containing 5 black and 5 white balls and placed into
a yellow urn initially containing 5 black and 3 white balls, what is the probability that the yellow urn will contain an equal number of black and white balls after this change?

Ans:[spoiler]2/9[/spoiler]
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by manpsingh87 » Sun May 22, 2011 11:06 pm
sampath wrote:If two balls are randomly drawn from a green urn containing 5 black and 5 white balls and placed into
a yellow urn initially containing 5 black and 3 white balls, what is the probability that the yellow urn will contain an equal number of black and white balls after this change?

Ans:[spoiler]2/9[/spoiler]
out of 10 balls any two balls can be selected in 10C2 ways;
now yellow urn will contain equal black and white balls if the two drawn balls are white;

therefore probability of drawing 2 yellow balls from the green urn is 5C2;

hence required probability is 5C2/10C2= 2/9
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by Anurag@Gurome » Sun May 22, 2011 11:08 pm
sampath wrote:If two balls are randomly drawn from a green urn containing 5 black and 5 white balls and placed into
a yellow urn initially containing 5 black and 3 white balls, what is the probability that the yellow urn will contain an equal number of black and white balls after this change?

Ans:[spoiler]2/9[/spoiler]
Yellow urn will contain an equal number of black and white balls, only when the 2 balls drawn will be 2 white balls.
So, Probability of drawing 2 white balls from green urn = Probability that the yellow urn will contain an equal number of black and white balls = 5C2/10C2 = [spoiler]2/9[/spoiler]
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