Another Probability Problem

[Xonian]

I would really appreciate some help with this problem, number 45. The answer is at least seven. How? Thanks!

 

[pka]

I would really appreciate some help with this problem, number 45. The answer is at least seven. How? Thanks!

In order to get the suggested answer we must make several assumptions.
Assume that the problem is about one guess out of the total possible.

Now for any $\displaystyle n\in\mathbb{Z}^+$ then there are $\displaystyle 3^n$ possible pass words.

So solve $\displaystyle 3^{-n}\le 10^{-3}$.

 

[HallsofIvy]

In order to get the suggested answer we must make several assumptions.
Assume that the problem is about one guess out of the total possible.

Now for any $\displaystyle n\in\mathbb{Z}^+$ then there are $\displaystyle 3^n$ possible pass words.

So solve $\displaystyle 3^{-n}\ge 10^{-3}$.

Typo: you mean $\displaystyle 3^{-n}\le 10^{-3}$ or $\displaystyle 3^n\ge 10^3$.