This was a thought experiment I had many years ago.
Suppose a village has two high schools, one key high school and one regular high school, each recruiting 500 students. If 1,000 students pass the high school entrance examination, the top 500 will inevitably enter key high schools, and the last 500 will enter ordinary high schools. These students have gone through high school and taken the college entrance examination. Eighty per cent of graduates from key high schools go to university, while only 8 per cent of graduates from regular high schools go to university.
All this seems normal, and the probability of admission to key high schools is 10 times higher than that of ordinary high schools, and students and parents are flocking to it. But think about it carefully, the last 20% of key high schools failed the college entrance examination, and when these people took the high school entrance examination, their scores were higher than those of everyone in ordinary high schools, and they must be higher than the 8% of successful students, but they failed in the college entrance examination, which can also be said to have lost to the 8%.
Speaking of which, the paradox appears, if you get the 500th place in the high school entrance examination, then you go to a key high school, and you must improve your grades by 20% before you can be admitted to university; If you go to a regular high school, you can get into college as long as your grades don't drop by 8%. So is it the high probability of going to a key high school, or is it a high probability of going to a regular high school?