Question

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, and you should explain how you got it.

Answer 1

P( rolling 6) = 1/6
P(NOT rolling 6) = 5/6
P(AT least one 6) = 1 - 5/6
P(After x number of trials to obtain at least one 6) = 0.9
Then 0.9 = 1 - (5/6)ˣ

0.9 - 1 =  - (5/6)ˣ
- 0.1 =  - (5/6)ˣ   → (5/6)ˣ = 0.1

x(ln 5/6) = ln(0.1)

x = ln0.1) / ln(5/6)  = 12.63 ≈ 13 times

Answer 2

What does the "In" mean when, for example, you say (In5/6)