Okay, so I'm a science teacher and I'm teaching genetics. We were talking about the Law of Independent Assortment, which states that each chromosome is sorted into gametes independently.

In other words, we (humans) have 46 chromosomes, but we only have 23 *types* of chromosomes. We have two copies of each chromosome, and we get one from each parent. So for each chromosome, from each parent, you can think of it as a coin flip. You either get version 1 or version 2, and which you get is random, and the chance is independent of each other chromosome.

This is great, because you can think of the chances of getting an individual chromosome from a parent as a 50/50 coin flip.

So I had a student ask, what are the chances that two siblings will be identical twins even though they weren't born at the same time? Basically, what is the chance that all those coin flips came out exactly the same twice.

I obviously couldn't answer this on the spot, I had to think a bit. So here's how far I got.

1) Each chromosome is a coin flip. So each is a 50% chance (0.5).

2) For any child you flip the coin 46 times, 23 from one parent and 23 from the other.

3) To simplify thinking I imagined, what if the coin flipped "heads" 46 times in a row? It doesn't actually matter if it *was* heads 46 times in a row, the values could be anything, but they need to be duplicated and so thinking of it as all heads helped me. But basically then the question is, what are the chances that would happen *again*?

4) Instead of thinking of it cumulatively, my understanding is the right way to think about it is 46 *pairs* of flips. In other words, what are the chances that Chromosome A1 from the father is heads twice? That would be (0.5 * 0.5=0.25). So a 25% chance *per chromosome*.

5) You have to do that 46 times. And now we're getting into where my math gets fuzzy but I'm thinking to calculate that you would do (0.25^46). That would be 0.25 multiplied by itself 46 times (one time per chromosome). That maybe way off though?

What I get from that is around 2.02x10^-28. So, yeah, that's a veeeeeeeeery small chance.

I think I can say right away there's basically no chance that two people born from the same parents are identical twins by chance. I know it would be difficult to apply the question to the population of Earth, because it wouldn't be as simple as saying out of the 8 billion people and applying the odds, because you only get this chance for a child born *that has a sibling*.

Anyway, I may already be way off since I'm out of my depth. Any feedback? My student is waiting patiently for an answer.
To clarify (since the bot asked me to) I want to know:

1) Is my 2.02x10^-28 answer in the right ballpark or is there something fundamentally flawed about my approach.

2) Does anyone have any ideas on how you would apply this to the actual population. Would you take that chance and then multiply it by the number of people alive today with at least one sibling? I imagine that information is at least roughly available and would be fun to throw in.

Thanks!