Six hundred chances are sold at $3 apiece for a raffle. there is a grand prize of $700, two second prizes of $200, and five third prizes of $50. first calculate the expected value of the lottery. determine whether the lottery is a fair game. if the game is not fair, determine a price for playing the game that would make it fair.

Expected net gain is -$0.75. Not a fair game. Appropriate price is $2.25.

Step-by-step explanation:

There is 1 in 600 chance to win the grand price (1/600)

There are 2 in 600 chance to win the 2nd price (2/600 = 1/300)

There are 5 in 600 chance to win the 3rd price (5/600 = 1/120)

We can use these probability to calculate the expected gain from this game

Since the cost to play is $3, the expected net gain from this game is

$2.25 - $3 = -$0.75

So this game is not fair as the player is losing money. The appropriate price should instead be $2.25