You have a bag containing 3 pancakes:

  1. Golden on both sides (GG)
  2. Burnt on both sides (BB)
  3. Golden on one side and burnt on the other (GB)

You shake the bag, draw a pancake at random, observe one side is golden, and are asked:

What is the probability that the other side is also golden?

Step 1: Sample Space of Sides

Each pancake has two sides, so the total sample space of visible sides is:

  • GG pancake: 2 golden sides
  • BB pancake: 2 burnt sides → irrelevant here
  • GB pancake: 1 golden, 1 burnt side

So among the 6 sides (2 per pancake), there are:

  • 3 golden sides in total:
    • 2 from GG
    • 1 from GB

These 3 golden sides come from:

  • 2 instances of GG
  • 1 instance of GB

Step 2: Conditional Probability

You’re told a golden side is observed. So the sample space is restricted to:

  • GG’s 2 golden sides
  • GB’s 1 golden side

There are 3 equally likely golden-side observations:

  • GG-side 1
  • GG-side 2
  • GB’s golden side

In how many of these is the other side also golden?

  • GG: yes, both sides golden (2 outcomes)
  • GB: no (1 outcome)

So:

\[ P(\text{other side is golden} \mid \text{observed golden}) = \frac{2}{3} \]

Final Answer

\[ \boxed{\frac{2}{3}} \]

Reference