Question

In: Statistics and Probability

Chicago is a group dice game that requires no skill. The objective of the game is...

Chicago is a group dice game that requires no skill. The objective of the game is to accumulate points by rolling certain combinations (GamezBuff, 2017). How do you play Chicago? There are eleven rounds in the game, one for each combination that can be made by adding two dice, namely the numbers two through 12. Each round has a target combination starting with two and going up all the way to 12. Going clockwise, the players take turns to roll both dice one time. If players roll the target combination, then they score points equal to the target combination, otherwise they score zero. For example, if the round corresponds to target combination six, then the player scores six points if the two dice add up to six. Else, the player scores no points. The player with the highest score at the end of the eleventh round wins the game.

What is the probability that the player rolls the target combination given that he/she rolled a one?

Solutions

Expert Solution

Probability of any number being the  target combination is 1/11.

If one dice is a 1, and the other dice can be any number, so the maximum target combination that can be reached is 7.

So, Probability that the target combination was 2 and the target combination is reached =

Probability that the target combination is 2 * the number of second dice is 1.

= 1/11 * 1/6 = 1/66

So, Probability that the target combination was 3 and the target combination is reached =

Probability that the target combination is 3 * the number of second dice is 2.

= 1/11 * 1/6 = 1/66.

Probability that the target combination was 4 and the target combination is reached =

Probability that the target combination is 4 * the number of second dice is 3.

= 1/11 * 1/6 = 1/66.

Probability that the target combination was 5 and the target combination is reached =

Probability that the target combination is 5 * the number of second dice is 4.

= 1/11 * 1/6 = 1/66.

Probability that the target combination was 6 and the target combination is reached =

Probability that the target combination is 6 * the number of second dice is 5.

= 1/11 * 1/6 = 1/66.

Probability that the target combination was 7 and the target combination is reached =

Probability that the target combination is 7 * the number of second dice is 6.

= 1/11 * 1/6 = 1/66.

The probability of reaching the target if the target was greater than 7 is 0, because we cannot have more than 6 on the other dice.

So, total probability that the player rolls the target combination given that he has rolled one =

= 1/66 + 1/66 + 1/66 + 1/66 + 1/66 + 1/66

= 6/66

= 1/11

= 0.0909.

IF YOU FIND THIS ANSWER HELPFUL, PLEASE UP VOTE.


Related Solutions

Chicago is a group dice game that requires no skill. The objective of the game is...
Chicago is a group dice game that requires no skill. The objective of the game is to accumulate points by rolling certain combinations (GamezBuff, 2017). How do you play Chicago? There are eleven rounds in the game, one for each combination that can be made by adding two dice, namely the numbers two through 12. Each round has a target combination starting with two and going up all the way to 12. Going clockwise, the players take turns to roll...
Objective Make a function to serve as a Craps dice game simulator. If you are not...
Objective Make a function to serve as a Craps dice game simulator. If you are not familiar Craps is a game that involves rolling two six-sided dice and adding up the total. We are not implementing the full rules of the game, just a function that returns the value of BOTH dice and their total. Details In the function you create: Make a function that uses pointers and pass by reference to return THREE separate outputs (arrays are not allowed)....
  Python-“Ship Dice” Ship Dice: Ship Dice is a game that you will be creating. The rules...
  Python-“Ship Dice” Ship Dice: Ship Dice is a game that you will be creating. The rules of the game are fairly simple. The game is normally played with 2-6 people, but our version will only be one player who is playing. The rules are simple, player rolls 3 dice randomly (Red, Green, and Blue), and the player has couple of options to choose from to win: 1- 3 chances to roll the dice randomly and get all dices 6 2-...
PYTHON GAME OF PIG The game of Pig is a simple two player dice game in...
PYTHON GAME OF PIG The game of Pig is a simple two player dice game in which the first player to reach 100 or more points wins. Players take turns. On each turn a player rolls a six-sided die. After each roll: a) If the player rolls a 1 then the player gets no new points and it becomes the other player’s turn. b) If the player rolls 2-6 then they can either roll again or hold. If the player...
We will simulate a dice game in which 2 dice are thrown. If the roll is...
We will simulate a dice game in which 2 dice are thrown. If the roll is 7 or 11, you win. If the roll is 2, 3, or 12, you lose If the roll is any other value, it establishes a point. If with a point established, that point is rolled again before a 7, you win. If, with a point established, a 7 is rolled before the point is rolled again you lose. Build your algorithm incrementally. First write...
Game of dice - fair dice: If I throw a number >= 5 I win. If...
Game of dice - fair dice: If I throw a number >= 5 I win. If he throws a number =< 4 he wins. I throw the first dice. Given that he loses(throws a number >4) what is the probability of me winning ? What is the expected number of throws before either of us wins?
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?
Fair game: The game with expected earning/loss equal to zero. A dice game costs $10 to...
Fair game: The game with expected earning/loss equal to zero. A dice game costs $10 to play. You get to roll two dice and if you roll a 2 or a 12 you win $100, if you roll a 7 you win $20 and there is no prize otherwise. Is this a fair game?
Dice Game Rules: 2 - 4 players Each player has 5 Dice. The dice have 6...
Dice Game Rules: 2 - 4 players Each player has 5 Dice. The dice have 6 sides. Each player rolls their dice, and the dice statistics are reported: Sum, number of pairs (and of what), and "straights" - (all dice in order - e.g. 1,2,3,4,5 or 2,3,4,5,6) Player 1 might roll 2,2,3,4,4 so the results would be: Sum: 15, 1 pair (2), 1 pair (4) Player 2 might roll 1, 1, 4, 6, 6 so the results would be: Sum:...
You pay $1 to play a game. The game consists of rolling a pair of dice....
You pay $1 to play a game. The game consists of rolling a pair of dice. If you observe a sum of 7 or 11 you receive $4. If not, you receive nothing. Compute the expected value and standard deviation for this game?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT