If x is the net gain to a player in a game of chance,then E(x)is usually negative.This value gives the average amount per game the player can expect to lose over the long run.A service organization is selling $2 raffle tickets as part of a fundraising program.The first prize is a boat valued at $2910,and the second prize is a camping tent valued at $400.In addition to the first and second prizes,there are twenty $24 gift certificates to be awarded.The number of tickets sold is 3000.Find the expected net gain to the player for one play of the game.Round your answer to the nearest cent.
A) $1,109.33
B) $1.34
C) $0.74
D) -$0.74
E) -$1,109.33

Question

If x is the net gain to a player in a game of chance,then E(x)is usually negative.This value gives the average amount per game the player can expect to lose over the long run.A service organization is selling $2 raffle tickets as part of a fundraising program.The first prize is a boat valued at $2910,and the second prize is a camping tent valued at $400.In addition to the first and second prizes,there are twenty $24 gift certificates to be awarded.The number of tickets sold is 3000.Find the expected net gain to the player for one play of the game.Round your answer to the nearest cent. ​
A) ​$1,109.33
B) ​$1.34
C) ​$0.74
D) ​-$0.74
E) ​-$1,109.33

Quizplus · Accepted Answer

To find the expected net gain to the player, we need to find the expected value of x which is the difference between the cost of the ticket and the amount the player can expect to win. 
The cost of the ticket is $2. 
The probability of winning the first prize is 1/3000 and the value of the prize is $2910. 
The probability of winning the second prize is 1/3000 and the value of the prize is $400. 
The probability of winning a gift certificate is 20/3000 and the value of each certificate is $24. 
So,

E(x) = (1/3000)(2910) + (1/3000)(400) + (20/3000)(24) - 2 
E(x) = 0.97

This means that the player can expect to lose about $0.97 per game on average. Therefore, the best choice is D, -$0.74 (rounded to the nearest cent).

If X Is the Net Gain to a Player in a Game