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A point (x,y) is randomly selected such that 0 <= x <= 3 and 0 <= y <= 6. What is the probability that x + y <= 5? Express your answer as a common fraction.

 Jul 9, 2022
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There are infinite amount of values for x and y we can choose, suggesting the use of geometric probability. The area of (x, y) we can choose is a rectangle with the x width being 3 and the y length being 6. Let's the draw the line x + y = 5. Note that this creates similar triangles. 2/5 = x/5 which results in x = 2. There area of the big triangle - the area of the small triangle would be the area where we would get succesfful outcomes but still inside the rectangle.

 

This is:

25/2 - 4/2 = 21/2

 

Because the total area for the x and y values is 18. Our probability is 7/12. 

 Jul 10, 2022

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