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

no

"Fair" from whose viewpoint — the buyer or the seller? Aren't those who sell the tickets entitled to a profit for selling 250 tickets? Do they actually sell all 250 tickets?

When you invest in a 50/50 raffle, the group selling the tickets gets 50% of the proceeds rather than 20%.

This will probably make your answer less certain, but I hope it helps you understand the situation better.