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Fair price

aburchett

New member
Joined
Jan 19, 2011
Messages
48
A community 5K run will award $50 to the winner. 80 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.

My work:

Probability of winning= 1/80
Probability of losing= 79/80

E=P(wins)(amount won) + P(loss)(amount lost)
E= 1/80 * 30/1 + 79/80 * -20/1
E= 3/8 + -158/8
E= -19.375
E is approximately -$19.38 this would be the total expectation

Fair price = expectation + cost to play
Fair price = -19.38 + 20
Fair price = $.62

Is this correct or where did I go wrong?
 

tkhunny

Moderator
Staff member
Joined
Apr 12, 2005
Messages
9,708
Looks fine, if that is the appropriate working definition of "Fair Price".
 
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