Statistics Help Requested (Discrete Distributions)

[nichojo]

Homework Statement

The problem:

An airline always overbooks, if possible. A particular plane has 95 seats on a flight and the airline sells 100 tickets.

If the probability of an individual not showing is 0.05, assuming independence, what is the probability that the airline can accommodate all the passengers who show up?

Homework Equations

Binomial and Poisson

The Attempt at a Solution

I tried taking the sum from 1 to 95 (X<=95) with a choose of (100, x) * (.95)^x * (.05)^(100-x)

with no luck. I've also tried numerous other sequences, but I feel I'm stuck.

Thanks in advance.

 

[ZioX]

What is the probability that 4 don't show up? 3? 2? 1? 0? Add them up.