This is much easier to intuit if I imagine 101 urns. One is 0% red, one 1% red, one 2% red, etc. If I choose one urn at random, and then the first ball I pick

This is much easier to intuit if I imagine 101 urns. One is 0% red, one 1% red, one 2% red, etc. If I choose one urn at random, and then the first ball I pick is red, odds are good I picked a red-heavy urn. I’d be interested to see if the general public answers differently when it is framed more concretely.