We have three pancakes. One is burnt on both sides, one is burnt on one side, and one is not burnt at all. The pancakes are stacked on a plate so that all that can be seen is a burnt side on top. What is the probability that the fully burnt pancake is the one on top?

Free worked solution · Quant Blueprint

2/3, assuming each pancake is equally likely to be on top and either side is equally likely to face upward.

1. Label the pancakes BB, BW and WW. There are six equally likely choices of top pancake and upward side.
2. The observed burnt top side leaves three possibilities: either face of BB, or the burnt face of BW.
3. Two of those three possibilities belong to the fully burnt pancake, giving probability 2/3.

Common mistake

After seeing a burnt side, BB and BW are not equally likely: BB has twice as many ways to produce that observation.

Follow-up

If the prior chance of BB being on top is a and of BW is b, with random orientations, the posterior is a/(a+b/2). The 2/3 result uses a = b.

Original educational explanation for this practice question. Reviewed 2026-10-13. Firm-style practice; the label describes the collection’s preparation context.