Originally Posted by Steady Eddy
But the OP didn't mention probability, he mentioned a paradox. A fail (1/n) followed by a success (1/n+1) seems to give greater weight to the second term. Why?
Say a coach has won 9 of 10 games for a 90% win rate. If he wins the next game, his rate becomes 91%, it only goes up 1%. But if he loses, his rate will be 73%, it drops nearly 18%! This doesn't seem fair. With a high success rate, new wins only improve it a tiny bit, but just one loss makes a huge drop. This lack of symmetry between wins and losses explains the puzzle the OP discussed, IMO.
Your example is true, but the OP is talking about probability. He says that you have a 40% success rate at something. That means the probability of you being successful is 40%. That is entirely different than you having been successful in 40% of your attempts as your example is stating. What you've said is what the OP is saying when he talks about a 40% average in a class being affected by getting a 50% on an assignment. That 40% is based on some prior successes and failures only. That is not the same thing as you being 40% likely to get a question right.