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Algebra

Blazing goIITian

Joined:	25 Jul 2011
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1 Feb 2012 21:09:30 IST

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~Probability! ANSWER~

Mathematics

A box contains 24 identical balls of which 12 are black and 12 are white.The balls are drawn at random from the box one at a time with replacement.The probability that a white ball is drawn for the fourth time on the seventh draw isAns=> 5/32

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hemang

Blazing goIITian

Joined: 27 Dec 2010

Posts: 1474

2 Feb 2012 10:53:51 IST

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if a black ball is drawn for the 4th time on the 7th draw that means in the preceeding 6 draws, we have drawn 3 black and 3 white balls. also the black balls are the same. and all the white balls are the same.

we have to arrange BBBWWW. the total number of ways is 6!/(3!*3!) = 6*5*4/3! = 20 ways.

also total ways to chose the first 6 balls is 2*2*2*2*2*2 = 64.

so the probability of getting 3 white balls and 3 black in the first 6 choices are =

20/64. also the probability to chose a black ball on the 7th choise is 1/2.

so the answer is 20/64 * 1/2 = 10/64 = 5/32.

this is an example of conditional probability.

sathyaram

Blazing goIITian

Joined: 25 Jul 2011

Posts: 322

4 Feb 2012 16:16:57 IST

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Dude,How to use latex and type things in it?

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