6 In my purse I have 10 circular coins of radius 123 10 res

6. In my purse I have 10 circular coins of radius 1,2,3, ..., 10, respectively. A pickpocket lifted my wallet (argh-h!) and fetched a random coin. What is the expected area of the coin?

6. In my purse I have 10 circular coins of radius 1,2,3, ..., 10, respectively. A pickpocket lifted my wallet (argh-h!) and fetched a random coin. What is the expected area of the coin?

Solution

given

In my purse I have 10 circular coins of radius 1,2,3, ..., 10, respectively. A pickpocket lifted my wallet (argh-h!) and fetched a random coin.

we have to find the expected area of the coin

as pickpocket fetched random coin so each coin has equal probability to be fetched

henc p=1/10=0.1

area of circle is given by area=3.14(r)²

then expected area of coin =0.1*3.14*(1+4+9+16+25+36+49+64+81+100)

                                       =0.314*385=120.89 answer