## A Better Bayesian Puzzle

### December 4, 2010

That last one got way too complicated!

Here’s the deal. I have two jars, each of which contains 100 marbles. The marbles are distributed like so:

Jar #1: 70 red marbles, 30 black marbles

Jar #2: 30 red marbles, 70 black marbles

While you weren’t looking, I drew one card from my well- and fairly-shuffled deck of playing cards, after saying to myself the following: “If I draw a club, I’m going to pick one marble at random out of the first jar. If I draw anything other than a club, I’m going to draw one marble at random out of the second jar.”

Now I present you with the results of that little procedure: One red marble.

What do you estimate as the probability that the card I drew was a club?

December 5, 2010 at 9:05 am

44%

December 5, 2010 at 1:23 pm

Thanks. Yeah I think this problem is better than the last one, because it’s much simpler but I still don’t think you can solve it just by guessing the right answer, so it illustrates the principle. You can’t solve this without using math, right?