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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.

 Oct 21, 2021
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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.

 

Sample space is represented by the area of the square, which is 4

The quadrant area includes all the favorable events.   x^2+y^2<= 1     ARea is    1/4 * pi *1^1 = pi/4

 

Probability of a favourable event is    pi/4 divided by 4     =    pi/16

 

 

 Oct 21, 2021

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