Geometric probability - line segmentOn the segment [0,1] two numbers X, Y are being randomly selected. Find the probability that X + Y ≤ 1 and X − Y &gt; 0.1.

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Geometric probability - line segmentOn the segment [0,1] two numbers X, Y are being randomly selected. Find the probability that   X  +  Y  ≤  1 and   X  −  Y  &amp;gt;  0.1.

n8ar1val · Accepted Answer

Step 1Lets draw a plane and use the x-coordinate of any point as the value of the number X and y-coord as a value of Y so that every point &quot;equals&quot; one pair of numbers. You know that both X and Y are between 0 and 1, so we draw a square with the side-length of 1 as a hole field of possible outcomes. We now should draw the situations that fit our requests. All of the &quot;good&quot; points should be below the line   y  =  1  −  x as we want that sum to be less or equal to 1. Step 2On the other hand, we want   X  −  Y to be greater than 0.1 so the points should also be to the right of the line   y  =  x  −  0.1 (so while the y is the same as on the line x gets greater). We get an area fenced by all our lines that fits our requests. Thus we calculate its area and divide it by 1 as that&#039;s the area of a hole square

Cale Terrell · Accepted Answer

Step 1lets say we have to choose two variables x and y from [0,1]. it can be demonstrated on 2D graph. the total number of pairs of points(x,y) where x,y are in range[0,1] may be represented by the area of square formed by lines   x  =  1  ,  y  =  1  ,  x  =  0  ,  y  =  0. This area (which is 1 square unit) represents the total possible combinations of x and y such that x is in[0,1] as well y.Step 2The points(or the combinations of x and y) which satisfies   x  +  y  ≤  1 are those points which are below the line   x  +  y  =  1 in the plane.and likewise the points satisfying   x  −  y  &amp;gt;  0.1 lies below the line   x  −  y  =  0.1 in that plane. so the area representing the points which satisfy above all constraints lies between the lines   x  −  y  =  0.1  ,  y  =  0  ,  x  +  y  =  1 which is 0.2025 so the probability is equal to area representing allowed points divided by the area of total square   =  0.2025

On the segment [0,1] two numbers X, Y are being randomly selected. Find the probability that X+Y leq 1 and X-Y>0.1.

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