Smallest simulable probability

MediumProbability Brainteasers~4m

You want to simulate an event with probability exactly $p$ . Your only randomness is $2$ rolls of a fair die and $1$ flip of a fair coin. What is the smallest positive value of $p$ you can realize exactly?

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How many equally likely outcomes do $2$ dice and $1$ coin produce together?
$6\cdot6\cdot2=72$ atoms; every event's probability is a multiple of $1/72$ .

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0.0139 (± 0.0002)

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Smallest simulable probability

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