What is the likelihood of a single human gene to the same gene from the other human?
Assumptions

Let's assume that we can perfectly align all human genome and therefore calculate such statistics of identity.

Let's assume that the probability of identity of 99.9% is the same for neutral sequences than for coding sequences. This assumption is most likely wrong but there is no other way to answer the question with the data that are given to us. 

What is the question exactly?

Your homework question is a little unclear unfortunately. I don't know what is meant exactly by


  How likely is it that any single gene might vary from one individual to another?


Does it mean


  You randomly sample two humans and randomly sample one gene. What is the probability of perfect identity a this gene?


or does it mean


  You randomly sample one gene, what is the probability that all humans are identical for this gene?


I will assume it means the first one.

Step by step

I will go by subquestions to guide through the thought process! Try to answer the following questions one by one and you should be able to get to the final answer yourself


Randomly sample two individuals and randomly consider one nucleotide in their genome. What is the probability that this nucleotide is the same?
Randomly sample two individuals and randomly consider two nucleotides in their genome. What is the probability that these two nucleotides are the same?
Randomly sample two individuals and randomly consider n nucleotides in their genome. What is the probability that these n nucleotides are the same?
Randomly sample two individuals and randomly consider n nucleotides in their genome. What is the probability that these n nucleotides are different?
Randomly sample two individuals and randomly consider 3000 nucleotides in their genome. What is the probability that these 3000 nucleotides are different?


What answer did you get? If you got stuck somewhere, please let me know where!

Hints


No point about using a calculator, it will return Infinite or 0 at some point anyway!
Don't worry too much if you're not using all the numbers that are given to you!