Suppose someone gives you 4 to 1 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win ​$4 if you succeed and you lose ​$1 if you fail. What is the expected value of this game to​ you? Should you expect to win or lose the expected value in the first​ game? What can you expect if you play 100 ​times?

One option in a roulette game is to bet $20 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $20 you paid to play the game and you are awarded $20. If the ball lands elsewhere, you are awarded nothing and the $20 that you bet is collected. Find the expected payback for this roulette game if you bet $20 on red. The expected payback is $ (Round to the nearest cent as needed.)

Two coins are flipped. You win $1 if either 2 heads or 2 tails turn up, and you lose $3 if a head and a tail turn up. What is the expected value of the game?

In the game of roulette, one of the simplest bets is to wager on red. Here if you bet $1 and the ball lands on a red number in the wheel, then you will win $2 (i.e. profit $1). If the ball lands on a black or green space in the wheel, then you win nothing. What is the expected value on this bet? See the wheel below and show the work that you did to complete this problem. No work = no credit.

There are 12 slips of paper in a hat. I will let you reach in and grab one, without looking. An amount of money is written on each piece of paper. One has $100, two have $50, three have $20, and the rest have $–20. If your paper has a positive amount, I will give you that amount in cash. If you get $–20, you must pay me $20. Calculate the expected value of playing the game.

An exclusive raffle is being held where only 7 tickets are available. The raffle is free to enter. If you choose to play, you could win $7 or lose $3. Three tickets are winning tickets and you will win $7 if your ticket is drawn. Four tickets are losing tickets where you must pay $3 if your ticket is drawn. What is the expected return if you enter the raffle?

In a game, you roll a die. If you get a 1 or a 5, you would win $5. If you roll a 4 you win $15 and if you roll a 2, 3, or 6 you lose $10. What is the expected value of one roll of the die? Type a response