lean_workbook_plus_59457

$P\left(\frac{\pi}{4}\right)=\dfrac{\left(\frac{\sqrt{2}}{2}\right)^3\left(\frac{\sqrt{2}}{2}\right)^3}{\left(1+\left(\frac{\sqrt{2}}{2}\right)^6\right)\left(1+\left(\frac{\sqrt{2}}{2}\right)^6\right)}=\dfrac{\frac{1}{8}}{\frac{9}{8}\cdot\frac{9}{8}}=\dfrac{8}{81}$ .