Either you roll a 12-sided fair die once. Either you roll a 6-sided fair die twice.

So in which game are you more likely to get a total of 12? Or are they both equally likely?

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Solution

In the first $12$-sided die, there’s one side out of 12 that gives us a total of 12. Thus the probability is$${\displaystyle \frac{}{}}$$

In the second scenario, we roll a 6-sided die twice and wish to obtain a sum of 12. This is only possible if we roll a 6 twice. Thus, the probability is

Clearly 1/12 > 1/36.

Thus, the answer is the first game.

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