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, because if there are 250 tickets selling for $2 each, the grand prize should be $500. to be fair
Is it not fair for the organization selling the tickets to realize a profit? How is "fair" being defined?
To determine whether $2 was a fair price for Sam to pay for a ticket in this game, we can calculate the expected value. The expected value is the average value that Sam can expect to win or lose per ticket played.
To calculate the expected value, we need to consider the probability of winning and the amount that can be won or lost.
In this case, there is a total of 250 tickets being sold and only one grand prize of $400. Therefore, the probability of winning the grand prize is 1/250.
The potential loss is the $2 ticket price. The potential win is the $400 grand prize.
To calculate the expected value, we multiply the probability of winning by the amount that can be won, and subtract the probability of not winning by the amount that is lost:
Expected Value = (Probability of winning × Amount won) - (Probability of not winning × Amount lost)
Expected Value = (1/250 × $400) - (249/250 × $2)
Expected Value = $1.60 - $1.99
Expected Value = -$0.39
The expected value is -$0.39, which means, on average, Sam can expect to lose approximately $0.39 per ticket played.
Since the expected value is negative, it suggests that paying $2 for a ticket to play this game is not a fair price. Over the long run, Sam is likely to lose money on this game.