Tag Paradox

Boy or Girl Paradox

The “boy or girl paradox” is a well-known brain teaser by famous puzzle-maker Martin Gardner. It’s popularly considered a “paradox” because (1) it has a highly unintuitive solution, and (2) its ambiguous wording meant either of two solutions could be valid solutions.

This is a rewording of that brain teaser to eliminate some ambiguity from that original question:

Out of all families with exactly two children, we randomly pick one family that has at least one boy. What is the probability that both children in this family are boys?

Assume only for the purposes of this puzzle that a child can only be a boy or a girl, and that either possibility is equally likely.

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Berkson’s Paradox

Berkson’s Paradox is a counterintuitive or unexpected trend observed in a sample due to a particular type of selection bias. This bias arises when the sample is selected based on the combination of two characteristics.

Also known as Berkson’s bias or collider bias, Berkson’s Paradox pertains to situations where a group is selected based on the combination of two characteristics and results in some false observation of correlation between the two characteristics – the correlation might be observed in the sample only because those without those two characteristics were not selected to be in the group in the first place.

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Base Rate Fallacy

What is the Base Rate Fallacy?

In simple terms, it’s a common error we make in assessing likelihoods due to (a) over-emphasizing the rate of something within a group and (b) under-emphasizing how common that group is in the first place (i.e., the base rate).

For example, let’s say you see a chess set in a building with 1 avid chess player and 1000 other people. You might assume it belongs to the chess player, even though it’s more likely to belong to one of the others because there are so many of them – if only 1% of regular people own chess sets, there would likely be ~10 of them in a group of 1000, outnumbering the 1 chess player.

Sometimes also referred to as Base Rate Bias or Base Rate Neglect, this is a cognitive bias arising from the tendency to place too much emphasis on event-specific information, at the expense of relevant base rate information. Often this results in a sense of probabilities or rates that are very far from reality!

To understand what this means, let’s look at a few more examples:

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