An intriguing dilemma: B$_?$ Vs B$_{E}$

At this point a new box $B_E$ with equal number of black and white balls is shown to the audience. In contrast with B$_?$, everyone can now check its content (the box I actually use contains 5 White and 5 Black). In this case we are only uncertain about the result of picking a ball, and, again, everyone considers Black and White equally probable.

Then a new virtual lottery is proposed, with a prize associated to the extraction of White from either box. Is it preferable to choose B$_?$ or B$_{E}$? That is, is there any special reason to opt for either box? This time the answer is not always unanimous and depends on the audience. Scientists, including PhD students, tend to consider - but there are practically always exceptions! - the outcomes equally probable and therefore they say there is no rational reason to prefer either box. But in other contexts, including seminars to people who have jobs of high responsibility, there is a sizable proportion, often the majority, of those who definitely prefer B$_{E}$ (and, by the way, they had already stated, or accepted without objections, that Black and White were equally likely also from this box!)

The fun starts in case (practically always) when there are people in the audience having shown a strong preference in favor of B$_{E}$, and later I change the winning color. For example, I say, just for the sake of entertainment, that the prize in case of White was supposed to be offered by the host of the seminar. But since I prefer black, as I am usually dressed that way, I will pay for the prize, but attaching it to Black. As you can guess, those who showed indifference between B$_?$ and B$_{E}$ keep their opinion (and stare at me in a puzzled way). But, curiously, also those who had previously chosen with full conviction B$_{E}$ stick to it. The behavior of the latter is quite irrational (I can understand one can have strange reasons to consider White more likely from $B_E$, but for the same reason he/she should consider Black more likely from $B_?$) but so common that it even has a name, the Ellsberg paradox. (Fortunately the kind of people attending my seminars repent quite soon, because they are easily convinced - this is the simplest explanation - that, after all, the initial situation with $B_?$ is absolutely equivalent to an extraction at random out of 15 Black and 15 White, the fact that the 30 balls are clustered in boxes being irrelevant.)