In a game of “Chuck a luck” a player bets on one of the numbers 1...

In a game of “Chuck a luck” a player bets on one of the numbers 1 to 6. Three dice are then rolled and if the number bet by the player appears i times (where i equals to 1, 2 or 3) the player then wins i units. On the other hand if the number bet by the player does not appear on any of the dice the player loses 1 unit. If x is the players’ winnings in the game, what is the expected value of X?

a) Let x denote the players’ winnings in the game. Find the probability distribution of x and draw a graph of the probability distribution.

b) What is the probability that the player will win at least 2 units?

c) What is the expected value and the standard deviation of X?

d) In light of the results you obtained above, will you play this game? Explain your answer.

Solutions

Expert Solution

Complete solution is given in attached images:

Thank You...!

orchestra answered 1 year ago

Next > < Previous

Related Solutions

(3) In the game of Chuck-a-luck, a player places a $1 bet on a number from...

(3) In the game of Chuck-a-luck, a player places a $1 bet on a number from 1 to 6. Three dice are then rolled. The player wins $1 for each die with the number they bet upon on it. a. Construct the probability distribution that includes all four events in this game. b. What is the expected value of this game? c. Instead of $1, how much should be charged to make this a fair game?

In the carnival game chuck-a-luck, three dice are rolled. You make a bet on a particular...

In the carnival game chuck-a-luck, three dice are rolled. You make a bet on a particular number (1, 2, 3, 4, 5, 6) showing up. The payout is 1 to 1 if that number shows on (exactly) one die, 2 to 1 if it shows on two dice, and 3 to 1 if it shows up on all three. (You lose your initial stake if your number does not show on any of the dice.) If you make a $1...

Coin taking game This game is played between 2 players, player 1 and player 2. There...

Coin taking game This game is played between 2 players, player 1 and player 2. There are two piles of coins. The values of a coin can be any integer. Both players know the values of all coins in both piles. Player 1 makes the first move, and play alternates between the players. A move consists of taking a coin from the top of either of the piles (either player can take from either pile). The game ends when both...

In a dice game a player first rolls two dice. If the two numbers are l...

In a dice game a player first rolls two dice. If the two numbers are l ≤ m then he wins if the third roll n has l≤n≤m. In words if he rolls a 5 and a 2, then he wins if the third roll is 2,3,4, or 5, while if he rolls two 4’s his only chance of winning is to roll another 4. What is the probability he wins?

Consider the following two-player game, in which Player 1 is the IMF, and Player 2 is...

Consider the following two-player game, in which Player 1 is the IMF, and Player 2 is a debtor country. Reform Waste Aid 3, 2 -2, 3 No Aid -2, 1 0, 0 a) Compute all (pure and mixed) Nash equilibria. b) Do you think that the above game is the case of a resource curse? Interpret the game with a story of a resource curse.

In a carnival game, a player spins a wheel that stops with the pointer on one...

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 62 percent BLUE, 24 percent RED, and 14 percent GREEN. Note: Your answers should be rounded to three decimal places. (a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is...

In a carnival game, a player spins a wheel that stops with the pointer on one...

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 64 percent BLUE, 22 percent RED, and 14 percent GREEN. Note: Your answers should be rounded to three decimal places. (a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is...

In a carnival game, a player spins a wheel that stops with the pointer on one...

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 65 percent BLUE, 20 percent RED, and 15 percent GREEN. Note: Your answers should be rounded to three decimal places. (a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is...

In a carnival game, a player spins a wheel that stops with the pointer on one...

In a carnival game, a player spins a wheel that stops with the pointer on one (and only one) of three colors. The likelihood of the pointer landing on each color is as follows: 64 percent BLUE, 20 percent RED, and 16 percent GREEN. Note: Your answers should be rounded to three decimal places. (a) Suppose we spin the wheel, observe the color that the pointer stops on, and repeat the process until the pointer stops on BLUE. What is...

This is done in C++. This is a game where one player thinks of a number...

This is done in C++. This is a game where one player thinks of a number between 1 and a 1000 and the other player has to guess in 10 tries or less. Allow two variations: the computer to pick the number and the player guesses or the player to pick the number and the computer to guesses. 1 – Player one picks a number 2 – Player two guesses the number. 3 – Player one either confirms that the...

Subjects