Essay; show all work. A community 5K run will award $50 to the winner. 50 people enter the race, and they each pay an entry fee of $20. Assuming they are all equally likely to win, what is a fair price for the competition? Round to the nearest cent.

Question

anonymous · Answer

who wrote this it makes no sense

anonymous · Answer

if 50 people enter and the winner gets $50 then they should each pay $1

anonymous · Answer

lol its my professor who came up with questions..

anonymous · Answer

but they each pay 20 dollar entry fee..

anonymous · Answer

right which is why this line 
what is a fair price for the competition? 
doesn't really make sense.  that is the problem with trying to write word problems for probability.  you have to be very very careful not to end up being ambiguous

anonymous · Answer

i should tell my professor that.. lol  so the fair price for competition would be $1.00

anonymous · Answer

well if everyone paid a dollar and had an equal chance of winning, their expected value would be 0, and that is the definition of fair.  so yes.  but don't quote me because who knows...

anonymous · Answer

that is a loaded question... lol