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A point (x, y) is randomly chosen such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. What is the probability that y ≤ 4x?

 Aug 3, 2022
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See the graph here

 

https://www.desmos.com/calculator/nztbhkeg63

 

The total area  is a square with a side of 1

 

We have a right triangle  with  legs of  (1/4) and (1) which is  not  included in the inequality region

 

Its area  =  (1/2)(1/4) (1)  =  1/8

 

So....the probability  that   y ≤ 4x  is

 

[ 1 - 1/8)] / 1  =   7 / 8

 

 

cool cool cool

 Aug 3, 2022

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