Two barrels problem from the Intuitive Explanation (answered)

I’m not sure if I’m do­ing some­thing wrong here. EDIT: Yup, I’m al­low­ing my­self to be tricked.

I’ve fi­nally sat down to read­ing http://​​yud­​​ra­tio­nal/​​bayes care­fully, and I solved all story prob­lems so far with no trou­ble. How­ever, now I’m at this one:

Q. Sup­pose that there are two bar­rels, each con­tain­ing a num­ber of plas­tic eggs. In both bar­rels, some eggs are painted blue and the rest are painted red. In the first bar­rel, 90% of the eggs con­tain pearls and 20% of the pearl eggs are painted blue. In the sec­ond bar­rel, 45% of the eggs con­tain pearls and 60% of the empty eggs are painted red. Would you rather have a blue pearl egg from the first or sec­ond bar­rel?
A. Ac­tu­ally, it doesn’t mat­ter which bar­rel you choose! Can you see why?

This doesn’t look right to me.

In the first bar­rel, we have 18% blue eggs that con­tain pearls, and an un­known num­ber of blue eggs that do not con­tain pearls, any­where be­tween 10% (worst case) and 0%. Depend­ing on that, the pro­por­tion of blue eggs with pearls among all blue eggs can only be be­tween 18/​(18+10) = 64ish% in the worst case, to 100% in the best.

In the sec­ond bar­rel, we don’t know how many pearls eggs are blue. We do know there are 45% eggs with pearls al­to­gether, there­fore 55% with­out pearls, and out of the lat­ter 60% are red there­fore 40% are blue. That means we have 40%*55% = 22% empty blue eggs. Pearl blue eggs are any­where be­tween 0 and 45%, so from 0% to 45/​(45+22) = 67ish%.

Were we just sup­posed to con­clude that there isn’t enough in­for­ma­tion to an­swer that prob­lem? But I’d say “any­where be­tween 64% and 100%” is a bet­ter shot than “any­where be­tween 0% and 67%”. If I ac­tu­ally had to choose, and there were valuable pearls at stake, I’d choose the first bar­rel. Am I mak­ing some sort of a mis­take?