Ask the Wizard #361
Here are the averages of each type of score as well as total points per game.
- Touchdowns: 5.23
- Field goals: 3.78
- Safties: 0.03
- Average points: 45.96
Here is a breakdown of what happened after each touchdown.
- Extra point attempt successful: 82.5%
- Extra point attempt unsuccessful: 5.8%
- Two-point conversion attempt successful: 5.3%
- Two-point conversion attempt unsuccessful: 6.4%
Here are some success rates for field goals, extra points, and two-point conversions.
- Field goal attempt successful: 85.1%
- Extra point attempt successful: 93.4%
- Two-point conversion attempt successful: 45.2%
Here is my solution (PDF).
Two dice are rolled until one of the following events occur:
- A total of 12 is rolled
- A total of 7 is rolled twice, consecutively
What is the probability the total of 12 is rolled first?