The Advanced Placement Statistics Syllabus states that students need only know how to obtain geometric probabilities through simulation. The geometric setting is somewhat similar to the binomial setting, the basic difference being that the geometric setting does not have a fixed number of observations. The probability of success is the same for each observation.
Observations are independent.
The mean number of rolls for the 10 trials is 6.5. The State of California then randomly selects 6 numbers from the set. If you happen to match the six number chosen by the State, you win millions of dollars. That is, you would expect to have to play 18,009,460 times to get your first success. If you played once a week, you would expect your first success after 346,336 weeks, or 6,660 years.