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Question-55433




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

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