Conditional probability

A conditional probability asks what share of the cases satisfying one condition also satisfy another. Written P(A given B), the condition B does not adjust the answer, it replaces the population the answer is measured against. Every conditional probability question is a question about which denominator you are standing in.

That is why the effect can run either way. Conditioning can raise a probability, lower it, or leave it alone, depending entirely on how the condition interacts with the event. There is no rule of thumb, which is precisely why the arithmetic has to be done rather than intuited.

The single most important property is that the order is not symmetric. P(A given B) and P(B given A) are different fractions over different denominators, and in the cases interviewers like they differ by a factor of three or more. The two sentences are made of the same words, which is what makes swapping them so easy.

In practice, the fastest defence is to say the denominator out loud before computing anything. Out of the borrowers who were flagged, or out of the borrowers who defaulted, are different starting populations, and naming which one you are in usually resolves the question before any multiplication happens.