## Red and Blue Marbles

I have two urns, and 100 marbles. 50 of the marbles are blue, and 50 of the marbles are red.

You get to arrange all 100 marbles in the two urns. Every marble must go into one of the two urns, but other than that you can arrange them however you want.

Then, I’m going to randomly choose one of the two urns, and then randomly choose a marble out of that urn. I’ll pay you $100 if the marble I pick is red.

What’s the most you would pay to play this game?

Solution