### Brain Teasers

# Two Ones

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

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".

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".

### Hint

They seem to be equal, but they aren't.### Answer

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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