Question Number 55433 by peter frank last updated on 24/Feb/19
Answered by mr W last updated on 24/Feb/19
Commented by mr W last updated on 24/Feb/19
Commented by mr W last updated on 24/Feb/19
$${let}\:{CA}={x},\:{CB}={y} \\ $$$${AB}={d}=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$$${in}\:{xy}−{coordinate}\:{system}\:{each}\:{point} \\ $$$${in}\:{square}\:{a}×{a}\:{represents}\:{a}\:{point} \\ $$$${pair}\:{A}\:{and}\:{B}.\:{points}\:{in}\:{the}\:{shaded} \\ $$$${area}\:{represent}\:{point}\:{pairs}\:{A}\:{and}\:{B} \\ $$$${with}\:{AB}\leqslant{a}. \\ $$$$\Rightarrow{probability}=\frac{{shaded}\:{area}}{{square}\:{area}}=\frac{\frac{\pi{a}^{\mathrm{2}} }{\mathrm{4}}}{{a}^{\mathrm{2}} }=\frac{\pi}{\mathrm{4}} \\ $$
Commented by peter frank last updated on 24/Feb/19
$${thank}\:{you} \\ $$$$ \\ $$