My mental rounding capacaties are worse than I thought – the 96 put me way off. ]]>

Yes 4096 is the exact number if the 0.5 is correct. I just rounded it to 4000 – close enough. And yes that is the number the reporter is looking for. Problem is that it is the wrong number. If she had asked what is the probability that this woman will have 12 males then the method is a good one. But that is not what she is doing. She is looking at the woman after she has already had the 12 sons. There one has to ask what is the probability that this even will occur in the population in general. That is a different question and give a result much close to one. That was my main point. We all have a tendency to focus on what seems to be a rare event and then compute the probably of that rare event. That is backwards and neglects the fact that we have already seen the results before we did the statistical testing/computation.

Ravi and Berry,

I have made a number of simplifying assumptions. The probability of a male child is not 0.5. The experts tell us that the probability of a male child is slightly greater than 0.5. Then when one starts looking at distributions of children by sex for a given woman other factors come into play such as the decision process of the person involved. If parents decide they want at least one boy or at least one girl then the proportion of boy/girl two child families will not be 0.5 as one would expect as many of the families that would have boy/boy or girl/girl will have a third child.

And as you pointed out Berry some women/couples my be predisposed to having boys. There is no reason that probability has to be the same for each person. I’ve glossed over that. Likely the good old central limit theorem comes into play. With the size of the population these things tend to even out remarkably well.

]]>1/dbinom(x=12, size=12, prob=0.5)

and get 4096. So the odds are more like one in FIVE thousand, not four.

What’s wrong with that?

That’s the probability of having 12 successes in 12 trials, when the probability of success in each trial is 50%. Isn’t that exactly, what the reporter is looking for?

So if every country in the world had 10’000 couples with 12 kids, we would expect the average number of couples per country with 12 boys to be 2.

And by the way: as the binomial distribution is discrete, 12 heads IS a unique result (in statistical sense).

“If the subject of this story come to her attention when she had ten sons she could have written a similar story”.

Yes, but only with odds 1 in 1024. 5 times more likely, in the long run.