When to stop? In Exercise 27 of the Review Exercises for Part, we posed this question: You play a game that involves rolling a die. You can roll as many times as you want, and your score is the total...

When to stop? In Exercise 27 of the Review Exercises for Part, we posed this question: You play a game that involves rolling a die. You can roll as many times as you want, and your score is the total for all the rolls. But … if you roll a 6, your score is 0 and your turn is over. What might be a good strategy for a game like this?

You attempted to devise a good strategy by simulating several plays to see what might happen. Let’s try calculating a strategy.

a) On what roll would you expect to get a 6 for the first time?

 b) So, roll one time less than that. Assuming all those rolls were not 6’s, what’s your expected score?

 c) What’s the probability that you can roll that many times without getting a 6?