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## Two Ones

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #44413 Fun: (2.05) Difficulty: (2.11) Category: Probability Submitted By: shenqiang

Which is more likely to happen?

1) Roll a fair die 4 times and get at least one 1;
2) Roll 2 fair dice 24 times and get at least one "double 1".

Rolling a fair die once and failing to get a 1 has probability 5/6, and rolling 2 fair dice 6 times and failing to get a double 1 has probability (35^36)^6, which is slightly larger than 5/6.

Therefore, if you do each of the above 4 times and still fail to get a 1, the latter has a larger probability, therefore, the latter has a smaller succeeding probability than the former.

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