# Probability of being employed

Let's assume on given year you have a 3% chance of being fired , 97% of not being fired

What are the odd after 4 years you are still employed?

This is hard because you cannot be fired twice

Denote N=not fired, F=fired

for four years, we have the possible outcomes

NNNN

FNNN

NFNN

NNFN

NNNF

But once you're fired employment ceases.

y=years

here is my attempt at the problem:

$\frac{N^y}{Y*F*N^{(Y-1)}+N^Y}$

$$0.97 ^ 4 = 0.88529281 \approx 88,5 \%.$$
$$\frac{0.88529281}{1 - 0.88529281} \approx 7.71785,$$