Honestly, I reckon a cat could do this one, mutatis mutandis:
A barrell contains 25% diamonds, and 75% circles.
10% of the diamonds are blue, the rest are red.
80% of the circles are blue, the rest are red.
One of the objects is pulled out at random, and you're told the colour.
You can take a guess at the shape. If you're right, then you get $10, if you're wrong then you get a $1 for your trouble.
You do pretty well if you always guess circle. Can you do better?
In fact it could be argued that a cat is a mechanism for solving such problems, amongst others.