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Ask the Wizard #361

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.