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?
If he wanted the fun of playing this game and taking a chance, it was a fair price. However, if he wanted to take the grand prize, he threw his money away.
Odds of 1 out of 250 are pretty poor.
Thanks
To determine if $2 is a fair price to pay for a ticket to play this game, we need to calculate the expected value. The expected value represents the average amount a player would win, or lose, in repeated plays of the game.
In this case, there are 250 tickets being sold for $2 each, and the grand prize is $400. So, the probability of winning the grand prize is 1/250.
To calculate the expected value, we multiply the probability of winning by the value of the prize, and then subtract the cost of playing the game. In this case, the expected value can be calculated as follows:
Expected Value = (Probability of Winning * Value of Prize) - Cost of Ticket
Expected Value = (1/250 * $400) - $2
Expected Value = $1.60 - $2
Expected Value = -$0.40
The expected value is -$0.40, which means on average, a player would lose $0.40 per ticket. Since the expected value is negative, paying $2 for a ticket in this game does not provide a fair price, as the player is expected to lose money in the long run.
Therefore, $2 is not a fair price to pay for a ticket to play this game.