Probability of escaping modification

[Polymerist]

Q: Lets say I have an enormous set of polymer chains, and each chain has 100 identical repeat units. I subject these chains to conditions that result in 15% of the repeat units being modified. The average chain will therefore have 15 modified repeat units and 85 unmodified repeat units. Assuming that modification is totally random, and the odds of modification are not affected by previous modification on that same chain, what is the probability of finding a single chain with no modified units at all?

A: For any single modification event, the probability of avoiding modification is 0.85.
I think the expression for the probability of a 100-unit chain to be totally unmodified = 0.85^100.
This is a very small number indeed.

Since I'm more of a chemist than a mathematician, I suspect I'm being a bit simple here.
Anyone have better ideas?

 

[Cubist]

You are correct.

You might want to look up the "binomial distribution" if you want to calculate the probability of 1,2,... being modified.