When to use Binomial Distribution vs. Poisson Distribution? 
A bike has probability of breaking down $p$, on any given day.

In this case, to determine the number of times that a bike breaks down in a year, I have been told that it would be best modelled with a Poisson distribution, with $\lambda = 365\,p$.
I am wondering why it would be incorrect to use a binomial distribution, with $n=365$. After all, isn't Poisson really an approximation of a sum of Bernoulli random variables?
Thanks!

For Binomial, we assume the bike breaks in a given day and it doesn't break again that day (one Bernoulli trial). For Poisson, bike might get fixed and break yet again in the same day (as said by @JMoravitz). Still, if the chosen time interval (day is an arbitrary choice) is narrowed down to so small that likelihood of breaking twice becomes negligible, Binomial is the model for the distribution. In that case, however, the number of Bernoulli trials becomes very large, in which case the Binomial converges to Poisson distribution (Poisson limit theorem). And then, "it is best modeled as a poison distribution because the calculations are much simpler and the approximation is sufficiently close for large n" (@Graham Kemp)
