Wednesday, March 20, 2013

Revisiting the falling coconuts

In late November, there was a chance for people to win $550 million in the PowerBall Lottery. I wrote a post with some interesting statistics about the chances of winning. You can read that post here:

With all that being said, March Madness is upon us and I have filled out my bracket. I make not pretenses, when I complete this every year, I always end up in the middle of the pack of my friends in "scoring" the bracket. It got me thinking, could I ever pick a bracket that is 100% correct?

If we take a look at the design of the bracket (ignoring the play-in games of yesterday and today), there are 63 games that will happen. (If you need a bracket, you can get one here)

64 teams start the playing tomorrow in 32 games
32 winners will then play each other in 16 games
16 winners will then play each other in   8 games (Sweet 16)
8 winners will play each other in 4 games (Elite 8)
4 winners will play each other in 2 games (Final 4)
The 2 winning teams will then play 1 games for the National Championship

32+16+8+4+2+1=63 games

If we take power rankings and knowledge of teams out of if, the chance of any team winning is 1/2 (although we all know that no #16 seed has ever gotten out of the first round...)

If we take the probability of winning a game and then expand that through the 63 games, you will end up 1/2^63 or .5 raised to the 63 power.

If you evaluate that expression, you end up with an answer of 1 chance in 9,223,372,036,854,780,000. That is 1 in 9 QUINTILLION! (9.22*10^18)

Just to touch back at the PowerBall chance of winnings, you were 3 times more likely to die from a coconut falling on your head and killing you that picking the winning numbers for the PowerBall. The chance of winning the PowerBall was 1 in 175,223,510.

Compare the odds, friends! You are 52 billion times more likely to win the PowerBall than pick a bracket with 100% accuracy.

What does all this mean?

Coconuts are going to be raining down all over people!

Bring this to your classroom. What questions can we have kids investigate?

  1. How many USA (population thereof) would it take to equal the odds of 1 person randomly picking the a correct bracket?
  2. If chances were M&Ms, how many equivalents of Soldier's Field would be filled?
What questions can the students come up with in investigating these numbers?

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