Question Number 37168 by NECx last updated on 10/Jun/18
$${A}\:{stone}\:{is}\:{thrown}\:{into}\:{a}\:{circular} \\ $$$${pond}\:{of}\:{radius}\:\mathrm{1}{m}.{Suppose}\:{the} \\ $$$${stone}\:{falls}\:{uniformly}\:{at}\:{random} \\ $$$${on}\:{the}\:{area}\:{of}\:{the}\:{pond}.{What} \\ $$$${will}\:{be}\:{the}\:{expected}\:{distance}\:{od} \\ $$$${the}\:{stone}\:{from}\:{the}\:{centre}\:{of}\:{the} \\ $$$${pond}. \\ $$$$ \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left./\mathrm{3}\:{b}\right)\mathrm{1}/\mathrm{2}\:{c}\right)\mathrm{2}/\mathrm{3}\:{d}\right)\mathrm{1}/\sqrt{\mathrm{2}} \\ $$