Pancake Conditional Probability
You randomly choose one of three pancakes — GG, BB, or GB — then observe that the visible side is golden. What is the probability that the hidden side is also golden?
Condition on what you actually observed
Once you know the visible face is golden, count the equally likely golden-face observations.
GG pancake
2 golden faces
BB pancake
B
B
Cannot produce the observation G
GB pancake
B
1 golden face
After observing G, exactly 3 equally likely face-observations remain:
GG
golden face 1
other side = G ✓
GG
golden face 2
other side = G ✓
GB
golden face
other side = B
Try a simulation
Each trial randomly chooses a pancake and then a side. Trials where the visible side is burnt are discarded.
0Observed golden
0Other side golden
—Observed probability
Run trials to see the estimate approach 66.7%.