Statistics Help Requested (Discrete Distributions)

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The discussion revolves around calculating the probability that an airline can accommodate all passengers on a flight with 95 seats after selling 100 tickets, given a 5% no-show rate. The user attempted to use the binomial distribution formula but struggled to find the correct approach. They are specifically looking for the probability of different scenarios where 0 to 4 passengers do not show up. The conversation emphasizes the need for clarity in applying the binomial distribution to solve the problem. The key takeaway is the importance of accurately calculating the probabilities for various no-show scenarios to determine overall accommodation likelihood.
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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.
 
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What is the probability that 4 don't show up? 3? 2? 1? 0? Add them up.
 

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