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What were the average number of touchdowns, field goals and safeties per game in the 2021 regular season? What was the success rate for field goals, extra points, and two-point conversions?

"Anonymous" .

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%

Two dice are rolled until a total of 12 appears three consecutive times. What is the average number of rolls required?

"Anonymous" .

363 + 362 + 361 = 47988

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?

"Anonymous" .

7/13 =~ 53.85%

Here is my solution (PDF).

This question is asked and discussed in my forum at Wizard of Vegas.