Suppose someone says that “The odds of a family having 3 children who are all boys is 1/8.” Taken literally, that would mean that 1/8 of all families ought to have exactly 3 boys and 0 girls. But that’s not true. Lots of families have fewer than 3 kids, or more than 3 kids.
A more correct statement would be that “If a family has exactly 3 children, the odds that they are all boys is 1/8.” And if X% of all families have exactly 3 children, then the odds of a family having 3 children who are all boys is (X%)*(1/8).
Sure. But I have never heard of a condition that causes this, in all my years of studying biology. If you have, then by all means enlighten me. I can’t think off the top of my head how it would work, though. At least in humans. The dad’s X chromosome is obviously viable, or dad would be dead. I suppose you could postulate some sort of extreme meiotic drive mechanism, but that generally only works in polar body-generating females. When spermatocytes go through meiosis, all four products mature into sperm cells, so you’d have to somehow kill off X-bearing sperm, presumably by having the Y chromosome code for some sort of toxic protein which could travel through the shared cytoplasm, but then since it IS shared, how would you prevent the toxic effect from spreading to the Y-bearing sperm? Hmm…
But, as I say, I’ve never heard of that happening.
There is also the issue of identical twins. If some among the 11 are identical twins then they should be counted as a single unit rather than 2 individuals in the calculations.
Here’s a link to a New York Times article on the subject, referring to a study published in Evolutionary Biology. Here’s the relevant quote:
“Mr. Gellatly found evidence that men carry a gene that determines the percentage of X and Y chromosomes in their sperm, and that the gene comes in three alleles, or versions. One produces mostly X chromosomes, another mostly Y, and the third yields equal numbers of both.”
Perhaps still more nitpickery: A more correct statement would be “If a family has exactly 3 children, the probability that they are all boys is 1/8.” While some people use the words “probability” and “odds” interchangeably, others (see, for example, Wikipedia) do not: they use the word “odds” to refer to the ratio of favorable to unfavorable outcomes, and would say that the odds of all boys would be 1 to 7.
The question that somebody SHOULD be asking is statistical rather than probabilistic - how many children of identical gender does one couple have to produce before you reject the notion that each conception FOR THAT COUPLE is an independent event with probability 0.5 of producing a child of either gender?
Not quite the same thing, but you could postulate that both parents each carry one copy of a recessive on the X chromosome that causes a very early miscarriage. Both parents are obviously viable, but the father contributes one copy of the recessive to each female embryo. About half the time, the mother will also contribute a copy. As a result, you would expect that roughly half of the female embryos would not be viable. It wouldn’t guarantee that all the kids would be boys, of course, but it would definitely change the odds.
That’s just a hypothetical case; I don’t know of any specific examples of such a situation.
I come from a family of five girls. Everyone I know with kids has one sex only, no mixed bags. The idea that men produce one sex over the other and resist regular probability seems plausible to me.
That depends on what you take as the prior for that possibility, which would probably be derived from study of large numbers of families.
If that were the case, then the father would be already dead. It’s not that you need two copies of a recessive gene for it to be active; it’s that you need to not have a dominant gene. Since the Y chromosome contains almost nothing, a man with a recessive gene on his X will always express it. This is why hemophilia and colorblindness, among others, are so much more common in men than women.
There is a link between the sex chromosome contained in a sperm and its motility, though I’m not well enough versed in the science to really be able to sum it all up. I think X-chromosome sperm tend to live longer (giving a longer window for successfully fertilizing an egg) but also tend to be slower (giving the boys a chance to get there first). Or perhaps it’s the other way around.
So it doesn’t have to be a matter of certain sperm not being viable, but rather that certain sperm have a lower chance of fertilizing an egg than others based on its “sex”. This is probably also strongly affected by the woman as well; the environment the sperm find themselves in will affect their survival and motility.
Anecdotally, I know of a family with 4 boys, but when the man remarried after a divorce, his new wife had 2 daughters by him.
For statistical purposes on a large population, the odds are generally considered 50-50 for either gender. (In actuality, there is a slight (about 5%) bias toward males, and a very small number who fit both or neither category).
But for any specific couple, there can be a significant bias toward either gender. Anecdotal stories of this are common. Personally, I know a neighboring family who had 7 boys, then later 1 girl. Famous families of mostly one gender are numerous: the Andrews sisters, the Jacksons, the Kennedys, etc.
This is well known in horse breeding. One of the common stats considered when evaluating a stallion is the gender percentage of his get.