This is not a homework question. It is actually kind of a biology question, but I'm dealing with the pure mathematics here. We came up with this reading "The selfish gene" by Richard Dawkins. He writes something like: "Elizabeth II is a direct decsendant William the conqueror.(adsbygoogle = window.adsbygoogle || []).push({}); However it is likely that they share not a single gene." This struck us as odd.

Being the only person in the room who knew advanced mathematics I took on the problem. Now I'd like to check if my solution is correct, because I feel I've got some flaws.

What my biologist friends told me is that one inherits 25000 genes from ones father. Also we counted that there are 30 generations between William and Elizabeth.

I think this would be analogous to flipping 25000 coins. All that end up heads one discards, and the ones that end up tail gets flipped again. What is the probability that after 29 throws we don't have a single coin that came up tail every time?

Doing some calculations I came up with a formula

[tex]25000\cdot0,5-\sum_{k=1}^{25000}(25000-k)0,5^{k+1}[/tex]

This should at least give the right answer for the first generation. Can I then just raise it to the power of 28 or should i do something different. Also, one problem is that when i tried to program this into matlab the first generation had a probability so close to one, it was one. Then rasing it to the power of anything won't give an accurate answer. This would say Dawkins was way of.

Any ideas?

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# Flipping coins

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