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.
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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.
Assuming the numbers are integers,
the following are the possible choices.
0 0 0 1 0 2
1 0 1 1 1 2
2 0 2 1 2 2
And the following are the sums of their squares.
0 1 4
1 2 5
4 5 8
The highlighted numbers are the sums which are no more than 1.
There are three out of nine, which makes the probability 33.33%.
π has nothing to do with this problem.
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