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A point (x,y) is chosen at random inside the square with vertices (0,0), (0,1), (1,1), (1,0). What is the probability that x^2+y^2<1?

Please explain because I want to know how you got the answer!

Apr 24, 2023

#1
+2

Note that the equation is a circle centered at (0, 0) with a radius of 1.

Using this, we can draw a diagram representing the outcomes: Basically, the shaded region (red) is the area of the success and the black square (side length 1) is the area of the total region

Can you take it from here?

Apr 24, 2023
#2
+1

I need the whole explanation.  This is due soon.

Can you give the complete explanation?

Guest Apr 24, 2023
#3
+2

Alright. Notice that the red-shaded region is a quarter circle with a radius of 1. This means that its area is $$(1^2 \pi) \div 4 = {\pi \over 4}$$

The area of the square is just 1 x 1 = 1, so the probability is just $$\color{brown}\boxed{ \pi \over 4}$$

BuilderBoi  Apr 24, 2023
#4
+1

Yes I can take it from here! Thank you so much for the answer and hint!

Guest Apr 24, 2023
#5
+2

Thank you!

BuilderBoi  Apr 24, 2023