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February 21st, 2013, 08:29 AM   #1
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Continuous Probability?

Person A chooses a random real number a from 0 to 2.

Person B choses a random real number b from 0 to 2.

What is the probability that | a - b | > 1/3

In words: What is the probability that the absolute value of the difference is higher than 1/3?

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I am not exactly sure how to get the final answer...

I tried to define a random variable Z to be Z = |X - Y|, where X and Y are random variables that denote the chosen real numbers. I had E_z denote the event that Z > 1/3 (first considered the converse, that Z \leq 1/3). I'm actually not a fan of the absolute value sign, so I thought it would be easier to consider the event that X - Y > 1/3 OR X - Y < -1/3.

I felt I was on the right path, but to no avail! Any help?
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February 21st, 2013, 09:02 AM   #2
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See this topic, where a method of solution has been given.
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