UNO High School Problem of the Week Competition

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Problem 2



During my weekly gambling trip to the casinos in Council Bluffs, I witnessed an interesting discussion. One group of gamblers insisted that, when 3 6-sided dice are rolled, a 9 and a 10 have an equally likely chance of appearing. Another group said that a 10 has a better chance of appearing than a 9.

Who's correct in this discussion? Formally, if I had a red die, a green die, and a blue die, and rolled them all simultaneously, what is the probability of rolling a 9? Of rolling a 10? Justify your answer with some computations - rolling 3 dice a large number of times will not suffice for this one.

Solution