This is a fantastic follow up question. The last ball is overwhelmingly likely to be red, though this is very counterintuitive. The “all-red” urn and the “all-r

This is a fantastic follow up question. The last ball is overwhelmingly likely to be red, though this is very counterintuitive. The “all-red” urn and the “all-red-but-one” urn were equally likely to be chosen at the start. But the draws have given you a lot of info about which distribution you’ve been drawing from. Were you sampling from the all-red distribution, your draws would be totally unsurprising — you would observe a run of 99 consecutive reds 100% of the time. If you were you sampling from the all-red-but-one distribution, however, you’d only have observed this outcome 1/100 times.