← The Last Card Problem · Lesson 1 of 3
Collecting is waiting
Roll a die and write down each face the first time it turns up. The first roll is always new. The second is new five times in six. By the time you have five faces, only one face in six is any use, so most rolls are repeats.
When something happens one time in n, you wait about n tries for it on average. That is why the end of a collection feels slow: every new card is rarer than the one before.
You have seen five of the six faces. On average, how many more rolls until the last one turns up?
A lesson is kept once you've answered the question and written at least 8 words. Nobody grades it; it stays on this device.