*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.*

This is probably another tricky math-logic thing that requires a meta view of Bayesian analysis or somesuch, but I don't come to the same conclusion.

ReplyDeleteWorking through this with an example . . .

Assume 200 shapes in the barrel.

Therefore, 50 Diamonds (D) and 150 Circles (C).

Therefore, 5 Blue Diamonds (BD) and 45 Red Diamonds (RD).

Therefore, 120 Blue Circles (BC) and 30 Red Circles (RC).

Consequently, for Blue, 5BD and 120BC. Total Blue: 125.

Consequently, for Red, 45RD and 30RC. Total Red: 75.

Given that they tell me the color, and I am to guess the shape:

If they tell me Blue, I guess Circle. My odds of winning are 120/125, or 96%.

If they tell me Red, I guess Diamond. My odds of winning are 45/75, or 60%.

Looks good to me! Told you it was easy.

ReplyDelete