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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.

1. What is the probability that the player rolls the target combination?

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Expert Solution

ANSWER::

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

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orchestra answered 1 year ago
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