Tricky abstract thinking Math problem. Probability question including an equation.

Question

Two values, $x$ and $y$ are selected at random and independently of each other from the interval. What is the probability.

The only idea I have thought of is using BinomPdf, but I still don't know how to implement that into this.

This is a question I am solving on my own that I have discovered. If you send the answer and work it would not assist me cheating or anything malicious.

@StinkingBishop I am not sure what happened some of it deleted. It should be fixed now. — Gaming Cobra, Feb 01 '20 at 21:23
https://math.stackexchange.com/a/2182328/638604 if I stated the equations and then say the probability is 0.25 would that be proper justification or is more info required. I want to show this to my teacher. (it is not a competition I discovered the question on my own and wanted to show it to my teacher) — Gaming Cobra, Feb 01 '20 at 21:53

score 0 · Answer 1 · answered Feb 01 '20 at 21:28

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View the two numbers as coordinates of a point in the unit square. The points of interest are above the line $y=x+\frac 12$ or below the line $y=x-\frac 12$. That is two triangles. Compute their total area and you have the probability as the area of the square is $1$.

answered Feb 01 '20 at 21:28

Ross Millikan

383,099

How would I compute the total area? how did you get the probability? Could you share your full length work? – Gaming Cobra Feb 01 '20 at 21:34
Just draw the picture of the square and the two lines. They cut off two triangles which are the area you want. – Ross Millikan Feb 01 '20 at 21:39
is the probability 0.25? – Gaming Cobra Feb 01 '20 at 21:48
Yes, it is. The idea of points in the square is a useful one for many 2D distributions – Ross Millikan Feb 01 '20 at 22:39

score 0 · Accepted Answer · edited Jun 12 '20 at 10:38

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As with many questions in mathematics, the best way to start is by making a picture!

Consider the following image, which I stole from an example given by Peter Woolfitt in this answer to an unreleated question.

Soltuion

As noted in the original source:

The [picture above] is the set of points $(x,y)$ such that $|x−y|\leq\dfrac{1}{2}$

The answer you are looking for is precisely the proportion of area that is white. Can you figure out what this is?

edited Jun 12 '20 at 10:38

Community

1

answered Feb 01 '20 at 21:30

Brian61354270

2,190

How would I find the area in the white? – Gaming Cobra Feb 01 '20 at 21:35
@GamingCobra Divide the square into four quadrants. Each white triangle occupies precisely half of the quadrant it lies in. – Brian61354270 Feb 01 '20 at 21:37
is the probability 0.25? – Gaming Cobra Feb 01 '20 at 21:48
@GamingCobra That is correct. – Brian61354270 Feb 01 '20 at 22:37

Tricky abstract thinking Math problem. Probability question including an equation.

2 Answers2