Is our children learning?

Contrary to what a Math PhD told me in an interview yesterday, the Law of Large Numbers does NOT say that if you have a sample from a population then the sample mean equals the population mean.  The Law of Large Numbers DOES say that as the sample size grows the sample mean will converge (in probability or almost surely) to the population mean.  To show that what the Math PhD said is obviously false imagine you have a sample of size one from a normal distribution.  It would be very surprising if your one sample point had a value equal to 0.  But that is what he told me.  I even probed him on his answer to see if he would revise it but he stuck to his definition.

I have been asking this question to prospective quants who say they have advanced degrees in Math or Stats.  So far I have two who answered correctly.  Two who confused the Law of Large Numbers with the Central Limit Theorem.  One who confused the Law of Large Numbers with the Central Limit Theorem and then stated the result of the CLT incorrectly anyways.  And then there was the above guy.

So "Is our children learning probability?"  Apparently no.