Graham_LRR said:
Your original reply to me had some stats, which I assume you've since removed.
You said there was a 50/50 chance of him having a blonde child, assuming he had a recessive gene.
Okay.
What are the chances of three blonde children?
That's where we were coming from.
Sorry, I removed a lot of it because I was worried I was just repeating what others had said. Now I feel like the final edit was harsher than I meant to be. Sorry about that. The video is otherwise funny, it's just that that joke doesn't particularly work if you really think about the science. (I still love you guys!)
As Anorgil says, it's 1/8. To put that in perspective, it's the same probability that all the children would be brunette (if the father has the recessive gene, which isn't too uncommon -- he's certain to have it if one of his parents was a blonde). You also said that they ALL must dye their hair, which is a much stronger statement than if you had said "it's unlikely that nobody in this family dyes their hair". The more relevant number is the 50/50, because if even one child is a natural blonde and all the rest dye their hair then what you said isn't true. In fact the probability that there would be AT LEAST one natural blonde out of three children (if the father has a recessive blonde gene) is 7/8.
Oh, unless the parents both have recessive red hair genes as well, in which case the probability is maybe a LITTLE lower because some children could potentially be redheads. If all three were redheads though, I'd check if the wife has a redheaded "friend".