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A point is randomly chosen inside a square of side length 2. What is the probability that the distance between the chosen point and the nearest corner of the square is between 1/2 and 1?

 Aug 22, 2023
 #1
avatar+126978 
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We can  consider  just a 1 x 1 square and  two  circles  with  equations  x^2 + y^2 =1  and x^2 + y^2 = 1/4

 

 

The area of the  smal square= 1

The area between  the  circles is   (1/4) pi ( 1^2  - (1/2)^2)  =  (3/4)pi / 4  = (3/16) pi

 

The probability  is  (3/16)pI / 1  ≈ .589 ≈  58.9%

 

cool cool cool

 Aug 22, 2023
 #2
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What would be the fractional answer though?

Guest Aug 22, 2023
 #3
avatar+126978 
0

3pi / 16

 

cool cool cool

CPhill  Aug 23, 2023

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