Product of Modes

In a game where two fair dice are rolled and the resulting score is calculated by multiplying the number on each die, what would be the product of all possible scores that have the maximum chance of being the outcome of this game?

Answer


The most frequent scores are 6 and 12 (each appearing 4 times out of 36 outcomes), so the product is

\[ 6 \times 12 = 72. \]
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