In these cases it's always good to think of extremes. For example for the Monte Hall problem imagine a million doors and all but one of them are opened, all emp

In these cases it's always good to think of extremes. For example for the Monte Hall problem imagine a million doors and all but one of them are opened, all empty, in any case. Then it's clear you originally had one in a million chances of picking the right door. Two ways to think about this (same conclusion): - Without loss of generality, take the case of just one red ball, rest are green. If you pick the one red ball on your first draw the chances are now 100% that the next ball is green (since there aren't any red ones left) whereas before you had picked the red one you had just a 99% chance of picking a green one. Hence after picking a red ball you are slightly more likely to pick a green ball next. - Another way to think of it, again without loss of generality consider if there was just one green ball and 99 red, then if you pick every one of them in some order there are a hundred different positions the green one could end up as. If you consider the one where it's last, after you have picked all but one (and they were all red), now you have a 100% chance to pick the green ball, even though you started out with 1% chance on the first draw: without loss of generality in the case of drawing until you reach the green ball when it is 1 in 100, each red ball you have drawn so far increases the chance of drawing the green ball next, up to a 100% chance when it is the only one left. Visualizing the chance going from 1% to 100% in this case as you draw more red balls should drive home the point that it becomes more and more likely you'll draw a green one next, in the cases that you've made it that far drawing red ones.)