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Two real numbers are chosen at random between 0 and 2. What is the probability that the sum of their squares is no more than 1? Express your answer as a common fraction in terms of pi.

 Jun 16, 2021
 #1
avatar+120930 
+2

See  here   :  https://www.desmos.com/calculator/n4del4rlti

 

If  x   =  one number  and  y  the other......we  have  the  area of a quarter-circle  of  a  radius of   1  centered at  the origin  ....  area   =  pi/4

 

And  the  total possible  area  =  a  2 x 2   square =   area of  4

 

So.....the probabilty  is

 

pi  / 4                       pi

_____       =         ____

    4                         16

 

 

cool cool cool

 Jun 16, 2021
 #2
avatar+9299 
+1

Totally wasn't thinking about using a graph for this...that makes so much more sense! surpriselaugh

hectictar  Jun 16, 2021
 #3
avatar+120930 
0

I just got lucky  ......LOL!!!!!

 

 

cool cool cool

CPhill  Jun 16, 2021

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