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You randomly select two distinct integers from 1 to 100. What is the probability that they differ by 1 or 2?

 May 5, 2020
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Intuitively...

 

You select any number, and there are, from 3 to 97,always 4 numbers satisfying this, so 4/100 = 1/25 probability that you get a difference of 1 or 2.

The probability of getting 3-98 is 96/100 = 48/50 = 24/25. Multiply together and get 24/625.

 

 

 

If you pick 2 or 99, with 2/100 = 1/50 probability, you get 3 numbers satisfying, so 3/100. Multiply together to get 3/5000.

 

If you pick 1 or 100, with 2/100 = 1/50 probability, you get 2 numbers, so 2/100 = 1/50. Multiply together = 1/2500

 

I'll let you add them together.

 

If you don't understand anythign feel free to ask.

 May 5, 2020

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