binomial OR poisson

[denian]

in a town, one of a hundred occupants loves fishing. what is the minimum occupants must be chosen so that the probability that there is at least one occupant who loves fishing is more than 0.7?

i hope u understand the question, because im doing some direct translation from my language to english.

ok. so, should i use poission or binomial. both lead to a very close answer. but which is more suitable. thx.

[grady]

Poisson is a suitable approximation to binomial when \lambda is small enough and n is large enough that \left(1-\frac{\lambda}{n}\right)^n\approx e^{-\lambda}, \frac{n(n-1)\cdots(n-i+1)}{n^i}\approx 1 and \left(1-\frac{\lambda}{n}\right)^i\approx 1. Poisson looks fine for this.

[denian]

thank you, grady