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Probability Creates a Problem

Questions from probability are really not that difficult as they appear to be. If you have a little command over Permutations and Combinations, then it is just a matter of a minute. But on the contrary, if permutations and combinations are confusing to you, then Probability too can become a nightmare. Though if you are lucky enough you may also see text questions of Favours & Odds, from where you can have a narrow escape.
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Problem : There are seven balls numbered 1 to 7, placed in a each of the two boxes coloured white and black. A ball is drawn out of white box and then from a black box. The process continues till the balls in any draw from both the boxes bear the same number. What is the probability that the balls will exhaust in the box before the process ends.

The solution to the above problem
does not need any hi-fi profile. Each one of you with a little understanding can solve this question. If I can frame a question, I hope you can frame a reasonable answer.
If you need help with any topic of maths, you are most welcome to mail me at solveaquestion@gmail.com
I shall be more than happy to help you out...

Have a Nice Concept Foundation.

IIT JEE EXAM 2011- EXAM DATE 10 April 2011, Last date to Apply = 15 December 2010

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