There had been a case in the UK where a woman's two babies died one after the other. Then some apparent statistician concluded 'If the chance of that occuring is 1 in a million, then she must have killed her babies'. Later, a very long court of law had been doing research on it and she appeared to be innocent because some clever statistician then concluded: "1 in a million in a population of 10 million means she likely did not kill her babies because the chance is great they die at birth, in her population".

My professor stated:

"If there is a 1/1000.000 chance of a baby dying at birth, then if the population is 10.000.000 people, such deaths occur very frequently because it happens 10 times in 10.000.000."

I don't understand this reasoning at all. How is 10 times in 10.000.000 considered as 'very frequent'? Completely illogical to me.

When I asked someone else, they said that you cannot state it is very frequent by that number alone and that you need a 'base amount' (cf. Base rate fallacy - Wikipedia, the free encyclopedia). Frequency should be relative to the base amount.

The relative frequency in this case is 10/10.000.000. The absolute frequency could perhaps be obtained by using Bayes' theorem?

I still don't understand the logic behind the claim that 10/10.000.000 is 'very frequent'.