I just watched a TV show that had a woman who allegedly had 11 children, all boys. Am I right in thinking that the odds of this happening are 1 in 2 to the 11th power or 1/2048? Certainly statisticly possible, but also definitively unlikely.
This is the important point. There are plenty of couples who are biologically incapable of producing children of one sex or the other. Doesn’t matter how many kids they have, they will always be all the same sex.
What do you mean by “definitively unlikely”? I don’t know how many women there are in the world who have 11 children, but it wouldn’t surprise me if the number were well over 2048. In that case, even if the probability of any one set of 11 children being all boys were 1/2048, it would be extremely likely that some woman, somewhere, had 11 boys.
Well, the OP asked for the odds of “this” happening. It’s unclear whether “this” refers to all the kids being boys or all being the same gender. So it’s either 1 in 2^10 or 1 in 2^11, depending on which one he meant.
Your odds are only for all families with eleven children. This has to be multiplied by the odds of a family having 11 children of any sex.
I think Needscoffee meant something like “What are the odds that any two people who start having kids will end up with exactly 11 kids of the same gender”. (I presume that this is a misunderstanding of the original question, which presumably is “Given that a couple has 11 kids, what are the odds that all 11 will be the same gender”.)