Difference between revisions of "2020 AMC 12B Problems/Problem 25"
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<math>\textbf{(A)}\ \frac{7}{12} \qquad\textbf{(B)}\ 2 - \sqrt{2} \qquad\textbf{(C)}\ \frac{1+\sqrt{2}}{4} \qquad\textbf{(D)}\ \frac{\sqrt{5}-1}{2} \qquad\textbf{(E)}\ \frac{5}{8}</math> | <math>\textbf{(A)}\ \frac{7}{12} \qquad\textbf{(B)}\ 2 - \sqrt{2} \qquad\textbf{(C)}\ \frac{1+\sqrt{2}}{4} \qquad\textbf{(D)}\ \frac{\sqrt{5}-1}{2} \qquad\textbf{(E)}\ \frac{5}{8}</math> | ||
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Revision as of 23:30, 7 February 2020
Problem 25
For each real number 
with 
, let numbers 
and 
be chosen independently at random from the intervals ![$[0, a]$](http://latex.artofproblemsolving.com/c/e/7/ce7d05d4da0d50abf77ee166ae0c6474bee5a1cf.png)
and ![$[0, 1]$](http://latex.artofproblemsolving.com/a/b/1/ab178d831a786b92cb4c9ddc2d33578223036f98.png)
, respectively, and let 
be the probability that
![\[\sin^2{(\pi x)} + \sin^2{(\pi y)} > 1\]](http://latex.artofproblemsolving.com/4/d/d/4dda018877a7b217408e61c488287f3bb9d31582.png)
What is the maximum value of 
