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Probability that 2nd ball differs by more than 2

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by saintforlife » Wed Aug 22, 2012 6:12 pm
Box of 10 balls numbered 1 thru 10. All have an equally likely chance to be selected. After you select one ball, what is the probability that the second ball selected differs by TWO or more.

Sorry, I don't have the answer or the source. But if someone can tell me the best and quickest way approach such problems, it will be awesome.

TIA!
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by Ian Stewart » Wed Aug 22, 2012 7:05 pm
We are just choosing two different integers from 1 to 10 inclusive, and want to know the probability they aren't consecutive. There are a few ways to do this, for example - we can choose 2 integers from 10 in 10C2 ways, so in 10*9/2 = 45 ways. That's our denominator. Now the only pairs of integers we don't want are the pairs of consecutive integers, so we want to rule out the selections {1, 2}, {2, 3}, {3, 4}, ... {9, 10}. So there are 9 selections we don't want, and thus 45-9 = 36 selections we do want, and the answer is 36/45 = 4/5.
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