This problem becomes much greater when the material is probability and when the example is something that the non-technical persons have been using for a while to assert their mastery of quantitative thinking.

Take, for example, the boy-girl problem: "one of two children is a boy, how likely is it that the other is also a boy?"

The right answer is one-half, though figuring that out requires some minimal understanding of probability, namely the difference between states and events and the mechanics of using prior and conditional probability to compute a posterior probability.

That computation is not the point.

The point is that even after this explanation, even in-person, some people think that they can argue for $1/3$. And that verb, "argue," is the problem.

Given a mathematical derivation yielding a result you don't like, the first step in a discussion of the result has to be pointing out the error in the derivation. My video does that for the $1/3$: the error is assigning "prior" probabilities after observing an event, in particular an informative event. (It's at the end of the computation because I need to introduce the basics of probability thinking first.)

But the people arguing for $1/3$ after that video never think they have to find the error; they either want both solutions to be valid (and don't understand why that's a problem, which is much more worrisome than not knowing how to think about probability) or appeal to some form of authority, like "I saw the $1/3$ on

*SciShow*and they have millions of views" (which is an even bigger problem and one that is widespread, probably a consequence of how science is being popularized).

For a successful technological society, reality must take precedence over self-esteem, for nature cannot be fooled, paraphrasing a much smarter person (last sentence of report).