Marie effectively labeled her blank die to ensure that the sums obtained when rolling alongside a regular die result in equally likely outcomes for all totals from 1 to 12. By marking three sides of the blank die with 6 and the other three with 0, she creates a scenario where the probability of rolling any specific total is uniformly distributed. Each possible outcome shows up exactly three times among the combinations available, thus satisfying the requirement of equal chances across all twelve sums.
In order to achieve an equal probability for all sums from 1 to 12 when rolling two dice, Marie labeled her blank die with three zeros and three sixes.
The special setup allows each of the twelve total sums to appear exactly three times, which is essential for maintaining equal likelihood.
The combinations leading to the totals perfectly showcase the power of probability, demonstrating that only specific arrangements can yield uniform outcomes across all sums.
By configuring the second cube with three faces as 6 and three faces as 0, the overall probabilities for each possible sum exactly balance at 1/12.
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