Probability of picking 2 numbers between 0 and 1 to be within 1/2 distance of each other?What's the probability of picking 2 numbers, x and y, between 0 and 1 such that they will be within the distance of 12 of each other?In other words, Pr ( distance between x and y ≤ 1 2 ) = ?I solved the problem through a geometric approach by rewriting the probability as Pr ( | x − y | ≤ 1 2 ) and graphing | x − y | ≤ 1 2 From the graph, I calculated the red area to be 75%.Question: What would be a non-geometric solution to this problem?

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Probability of picking 2 numbers between 0 and 1 to be within 1/2 distance of each other?What&#039;s the probability of picking 2 numbers, x and y, between 0 and 1 such that they will be within the distance of 12 of each other?In other words,   Pr  (  distance between x and y  ≤      1    2    )  =  ?I solved the problem through a geometric approach by rewriting the probability as   Pr  (      |    x  −  y      |    ≤      1    2    ) and graphing       |    x  −  y      |    ≤      1    2  From the graph, I calculated the red area to be 75%.Question: What would be a non-geometric solution to this problem?

iljovskint · Accepted Answer

Step 1If you pick two numbers greater than       1    2  , subtract       1    2   from the smaller of the two. If they are the same, subtract       1    2   from the first number. This is a bijection to the two numbers being over       1    2   apart.Step 2The probability of this not happening is   1  −            (              1        2            )        2    =      3    4

Probability of picking 2 numbers between 0 and 1 to be within 1/2 distance of each other?

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