Thinking
We love problems where reasoning matters more than speed or pattern knowledge. Sometimes we publish such problems - simply because we like them
You have two coins:
* Coin A: fair
* Coin B: heads with probability ( p \in (0.5, 1) )
You randomly choose one coin and flip it until you get a head.
👉 You see that the first head came on the 3rd flip.
1. What is the probability that you had a coin B?
2. How does the answer change as ( p ) increases?
3. Intuitively, why isn't it simply "the longer the delay, the more honest the coin"?
Note:
We're not looking for a "correct" answer. We want to understand how you think through problems with incomplete information.