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# Two numbers are successively selected at random and with

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Current Student
Joined: 31 Aug 2007
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Two numbers are successively selected at random and with [#permalink]  23 Oct 2007, 05:59
Two numbers are successively selected at random and with replacement from the set of integers { 1, 2, ... , 100 }. What is the probability that the first one is greater than the second?
Director
Joined: 13 Nov 2003
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Location: BULGARIA
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Hi
First the prob that both numbers are equal is 1/100.
Then the prob that both are different is 1-(1/100)=99/100
Either first or second will be bigger then the required prob is 99/200
Current Student
Joined: 31 Aug 2007
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I'm not really understanding this, but answer is 99/200.
Senior Manager
Joined: 11 Sep 2005
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young_gun wrote:
I'm not really understanding this, but answer is 99/200.

Let me try to explain this:

I suppose if we break it down into little simple form.....

Probability of selecting same numbers with replacement: P = (100/100)X(1/100) = 1/100

Now, probability of selecting different numbers with replacement = 1- (1/100) = 99/100

Now, probability of selecting TWO numbers when 1st one selected is bigger-

99/100 - includes both probabilities of selection either first one as bigger or smaller (In, TWO possible ways selection can be done with replacement)............so selection of first one ALWAYS bigger simply multiply (only half of the time) 0.5 to 99/100 = 99/200

I hope this will help!
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