Question

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 does not roll the target combination given that he/she rolled a one?

Answer 1

Here instead of finding the probability that the player does not roll the target combination given that he/she rolled a one, we'll find the probability of winning

Probability of rolling the target combination given that he/she rolled a one:

, similarly for 5 other combinations where he throws 2,3,4,5 and 6 in the second chance. Thus the probability of winning =

Thus the probability of losing = 10/11 which is equivalent to the probability that the player does not roll the target combination given that he/she rolled a one.