Problem 8. You play the following game with a friend. You each have a fair six sided die. Your friend rolls the die. You then roll the die at most two times. When you stop rolling, if you rolled a number higher than your friend's roll on your final roll, then you earn in dollars the difference between the die rolls. When you stop rolling, if you rolled a number lower than your friend's roll on your final roll, then you pay your friend in dollars the difference between the die rolls. When you stop rolling, if you rolled the same number that your friend rolled, then neither of you pay the other. What is the expected amount you earn per game if you optimally play a large number of games?

If P(AB)=0.7, is it possible that P(BA)=0.6? Explain

You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to flip a fair coin. She will give you $8$ for heads and $⁢22 for tails. Your mother says she wants you to roll a six-sided die. She will give you $4$ times the number that appears on the die. Determine the expected value of each game and decide which offer you should take.

You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $⁢4 times the number that appears on the die. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $⁢5 if the spinner lands on blue and $⁢15 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take.   The expected value for your sister's game: $$ The expected value for your mother's game: $$ Which offer should you take?

You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $5 times the number that appears on the die. Your mother says she wants you to flip a fair coin. She will give you $11 for heads and $19 for tails. Determine the expected value of each game and decide which offer you should take. Answer Кeypad Keyboard Shortcuts Expected value for your sister's game: $ Expected value for your mother's game: $ Which offer should you take? O your sister's offer O your mother's offer

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…

If a person rolls doubles when tossing two​ dice, the roller profits $ 65 ​, that​ is, the roller receives $ 65   more than the cost of the game. If the game is​ fair, how much should the person pay to play the​ game?

A pair of fair dice is rolled once. Suppose that you lose​ $8 if the dice sum to 7and win ​$13if the dice sum to 4 or 8.How much should you win or lose if any other number turns up in order for the game to be​ fair?

Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $17. If you roll a 3, 4 or 5, you win $4. Otherwise, you pay $2. %3D DDET