Please show as much work as possible to clearly show the steps you used to find each solution. If you plan to use a calculator, please be sure to clearly indicate your strategy.        Consider the following game.  It costs $3 each time you roll a six-sided number cube.  If you roll a 6 you win $15.  If you roll any other number, you receive nothing.   a) Find the expected value of the game.         b) If you play this game many times, will you expect to gain or lose money?

Please answer the question below. SHOW ALL WORK! A bag has 6 red marbles, 3 blue marbles, and 1 orange marble. In a game to raise money for a class trip; parents pay $5 and pull a marble randomly from the bag. The payout is $10 for pulling an orange marble, $4 for a blue marble, and $1 for a red marble. How much can the class expect to earn per game?

you are playing a game in which a single die is rolled. if a 2 or a 5 comes up, you win $24, otherwise you lose $3. what is the price that you should pay to play game that would make the game fair?

This game is called “Get Negative”.  Roll two dice (record these in the order you roll them), and then do then do the following:  take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score. Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above.  Tally the points and calculate the final score for each player.  Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.)  (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the…

This game is called “Get Negative”.  Roll two dice (record these in the order you roll them), and then do then do the following:  take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score.   Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player.  Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.)  (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the…

One option in a roulette game is to bet $7 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 $7 you paid to play the game and you are awarded $7. If the ball lands elsewhere, you are awarded nothing and the $7 that you bet is collected. Complete parts (a) through (b) below. III a. What is the expected value for playing roulette if you bet $7 on red? $ (Round to the nearest cent.) b. What does this expected value mean? Choose the correct statement below. O A. This value represents the expected loss over the long run for each game played. OB. Over the long run, the player can exper to break even. OC. This value represents the expected win over the long run for each game played.

Play this game with a partner. The first player marks down 1, 2, 3, or 4 dots on a sheet of paper. The second player then adds to this by marking down 1, 2, 3, or 4 more dots. The first player to exceed a total of 30 loses the game. Can the first player or the second player devise a surefire winning strategy? Explain carefully. Which player can definitely devise a surefire winning strategy? Use the Show Work learning aid to provide related calculations and additional reasoning to support your answer. O A. None B. The second player OC. Both OD. The first player

Can you explain it step by step? Thank you

A game consists of rolling a colored die with 3 red sides, 2 green sides, and one blue side. A roll of a red loses. A roll of a green pays $3.00. A roll of blue pays $8.00. The charge to play the game is $3.00. Would you play the game? Why or why not? Yes you should play. On any given roll the cost to play exceeds the amount you are expected to win. Yes you should play. On any given roll your expected value exceeds the amount that it cost to play the game. O No you should not play. On any given roll the cost to play exceeds the amount you are expected to win, O No you should not play. On any given roll your expected value exceeds the amount that it cost to play the game. O Yes you should play. You have a chance to win $8 and you only had to pay $2 to play.

Let’s examine the following game with a fair die. You select a number (not necessarilyan integer). I roll a fair die, and pay you $10, minus the square of the difference betweenyour guess and the number the die lands on. The game is played over and over again. Towin the most money in the long run, which number should you select? Explain.