I have an unlimited supply of standard 6-sided dice. What's the fewest number of dice that I have to simultaneously roll to be at least 90% likely to roll at least one 6?
You may use a calculator to help you with the computations if you like -- in fact you'll almost certainly want to -- but your final answer should be a positive integer.
This is the same as asking....What are the fewest number of dice that you must roll simultaneously to be at least 10% likely to roll no 6's ???
So we have
(5/6)^N = .10 take the log of both sides
N* log (5/6) = log (.10) divide both sides by log (5/6)
N = log (.10) / log (5/6) ≈ 12.6 ⇒ 13 dice