I can't resist interjecting here that the Poisson may indeed be a good choice of distribution here, despite the objections raised by meymathis. In fact, the Wikipedia page on the Poisson distribution (

Poisson distribution - Wikipedia, the free encyclopedia) cites a rule of thumb that the Poisson is an excellent approximation to the Binomial distribution if $\displaystyle n \geq 100$ and $\displaystyle np \leq 10$. Here we have $\displaystyle n = 100$ and $\displaystyle np = 1.667$, so both criteria are met.

If you "do the math" I think you will find that the answer to a) using the Poisson approximation is 0.1889 (as found by bondvista), and the answer using the Binomial distribution is 0.1862-- pretty close.