[Statistical Physics] No. of dice rolls so prob of getting a 6 is >90%

This question is really wearing me out, any ideas?

1. The problem statement, all variables and given/known data

How many times must I throw a fair dice in order to make the probability of getting at least one ‘6’ greater than 90%?
With this many throws, what is the probability of getting three ‘6’s?

It’s the first part I’m struggling with.

2. Relevant equations

The relevant question is the one on the top of the pic attached.

Where
P = probability of outcome interested in
N = number of throws

3. The attempt at a solution

Attatched.

I’m using P(1) as the probability of getting 1 six, so n=1.
For the second part of the equation I would use P(3).

Attached Images
File Type: jpg stats Q.jpg (45.1 KB)

http://ift.tt/1qGv7ek

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