You roll a fair die until you get a 6. What is the expected number of rolls?

You roll a fair die until you get a 6. What is the expected number of rolls?

Approach: This is a geometric distribution with success probability 1/6.

Expected value of geometric distribution is 1/p = 6.

Follow-up: What is the expected number of rolls to get two 6s?

Key concepts: geometric distribution, memoryless property.