SOLUTION: A lottery offers one 1000$ prize one 500$ prize and five 100$ prizes One thousand tickets are sold at 3$ each.Find the expectation if a person buys 1 ticket

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Question 1189209: A lottery offers one 1000$ prize one 500$ prize and five 100$ prizes One thousand tickets are sold at 3$ each.Find the expectation if a person buys 1 ticket
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Cost is $3
probability is 1/1000 of winning $1000, so x*p(x)=$1
and
1/999 of winning $500, or $0.501
and 5/998 of winning $100 or $0.501
E(x)=$2.002-$3=$0.998 or -$1.
1000 people spend $3 and receive $2000 in prizes, so the total expectation for the 1000 is -$1000.

Answer by ikleyn(52765) About Me  (Show Source):
You can put this solution on YOUR website!
.


            In this problem,  there are  two expectations. 


One expectation is the expectation to win.


Having one ticket of 1000 tickets, the probabilities are  

         1%2F1000  to win  $1000;

         1%2F1000  to win   $500;

    and  5%2F1000  to win   $100.


Therefore, the "expectation to win" is this amount


    expectation to win = %281%2F1000%29%2A1000 + %281%2F1000%29%2A500 + %285%2F1000%29%2A100 = 2 dollars.




The other expectation is the "expectation of the game".

It is equal to expectation to win  highlight%28MINUS%29  the price of one ticket, i.e.


    expectation of the game = $2 - $3 = - $1.



It means that playing the game many times, the gamer will lose, in average, 1 dollar per game.


Solved and thoroughly/carefully/comprehensively explained.


Find several distinctions/differences between my solution and the solution by @Boreal.