Question

sam bought 1 of 250 tickets selling for $2 in a game with a grand prize of 400 dollars. Was $2 a fair price to pay for a ticket to play this game?

Answer 1

The expectation value of the purchase was (1/250)*400 = $1.60.

Paying $2 for the ticket was fair. The organizer took in $500 and gave out one $400 prize. That only leaves $100, or 1/5 of ticket sales, for expenses and any charitable donation.