This is, arguably, the most wonderful math-time of the year. I just happen to be teaching probability during the NCAA tourney. It is the perfect one-two punch - math with a high level of engagement!
This all starts with a game of coin flipping. Who can be the best of the best at flipping coins? We discuss probability, make connections to powers of two, create tree diagrams... then March Mathness begins.
"Did you know that Warren Buffett has offered $1 billion to anyone that picks a perfect bracket?"
"Wow, that's crazy!"
"How can he afford that?"
"Can you do more than one bracket? That improves your chances!"
We go back to the probability of picking 4 flips correctly (1 in 16) and make some predictions. I have each student complete a region of the bracket, which is 15 games. They predict what the theoretical probability will be for getting all 15 games correct. Guesses range from 1 in 100 to 1 in 20000.
I let them on the calculator and they discover the answer: 1 in 32,768.
Ok that's a big number. so then we talked about the entire tournament: all 63 games. What is the theoretical probability of picking all 63 correct?
Students used some logic to say about 1 in 128,000 since 32*4 (regions) is 128. others went slightly higher: 1 in 1 million, 50 million. One student said 1 in 37 trillion. Students laughed and he did too, figuring he was way over the mark.
We then head over to Wolfram Alpha where we investigate large numbers.
Eyes go wide as jaws drop. Students try to decode how to say the number in front of them: 9,223,372,036,854,775,808
I line it up with the 37 trillion value to show the magnitude of a quintillion.
How do we quantify such a number? Well let's start with space. The distance from the sun to Neptune is about 2.8 billion miles. So how many inches is that? wow. that's a HUGE number. Why don't we write those as a ratio. What is the unit rate? 59,000?
Oh, so that means you are 59,000 times more likely to guess which inch I am thinking of than making a perfect bracket.
Well let's get crazier. The universe is 13.7 billion years old. Let's calculate how many seconds the universe been around? (mathy mathy converting process). Oh wow, that is about 432,043,200,000,000,000 seconds... That still isn't bigger than 2^63. But what does it mean?
TO RATIOS!
So if we compare the amount of seconds to the amount of brackets we get 4.68%.
WHAT DOES THAT MEAN?
That means... if... you started completing this 64-team tournament the moment the universe came into existence... and you kept filling them out, finishing one every second since the universe began. You'd be less than 5% of the way done.
They ponder, they think. They can't comprehend. How could they?
Eventually we'll get to compound probability where we multiply probability values to get the probability of two independent events. Then we'll take the probability of winning the Powerball and MegaMillion Lotteries on two consecutive days... and realize you are 100 times more likely to have that happen than pick a perfect bracket.
So. Why can Warren Buffett afford to give away $1 billion to a perfect bracket creator? Because so can you.
