In the game, Settles of Cataan’ you roll two 6-sided die and try to collect reso

Question

In the game, Settles of Cataan’ you roll two 6-sided die and try to collect resources based on what is rolled. You place game pieces on a 4 and a 6. ( remember a 4 can be rolled by have a 1 on the first die and 3 on the second die, or a 3 on the first die and 1 on the second die) a) What is the total number of combinations that can be rolled from 2 six sided die? b) What is the probability that on your turn, a 4 or a 6 is rolled? c) What is the probability that after a 4 or a 6 was rolled on your turn, a 4 is rolled on the next turn as well?

Explanation / Answer

a) Total number of combinations = 6*6 = 36

b) a 4 can be rolled in 3 ways i.e. (2, 2), (3, 1) and (1, 3) and a 6 can be rolled in 5 ways i.e. (3, 3), (4, 2), (2, 4), (5, 1), (1, 5)

Hence,

P(Rolling a 4 or 6) = (3 + 5)/36 = 8/36 = 2/9

c) P(4 on next turn and 4 or 6 was rolled on previous turn) = (3/36)*(2/9) = 1/54

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