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Two two-digit counting numbers (from 10 to 99, inclusive) were chosen randomly.These two integers could be the same or different. What is the probability that thedifference between these two numbers is at most 3?

 
 Sep 13, 2021
 #1
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The probability is 5/18.

 
 Sep 13, 2021
 #2
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Mmm

if the small one is 10  then the other can be 11,12 or 13   That is 3 possibilities

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from 11 to 95 inclusive there is 95-11+1=85 numbers each with 3 possible matches

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if the small one is 96  then the other can be 97, 98, 99   That is 3 possibilities

if the small one is 97  then the other can be 98,99   That is 2 possibilities

if the small one is 98  then the other can be 99   That is 1 possibilities

 

So I have  87*3+2+1 = 264 favourable pairs

 

Now there are 90 numbers to start with.  So 90C2= 4005  pairs are in the sample space

 

so the probability of the desired event happening is     264/4005 = 88/1335

 

I have not checked for silly errors.

 
 Sep 14, 2021

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