The NCAA basketball championship just wrapped up. It is always fun to fill out one of those tournament brackets to try to pick all the winners. It may seem easier than it really is. With millions of people filling out brackets every year, certainly a perfect bracket has been submitted, right? The truth is that there has never been a perfect bracket submitted. It all comes down to probability. I constantly try to challenge students in the classroom with math problems just like this. It helps to make a connection to the content we are learning.
Back to the probability problem. There are 64 teams that enter the single-loss elimination tournament. Since there is only one team that does not lose by the end, there are a total of 63 games throughout the tournament. So in order to fill out a perfect bracket, one must correctly predict the outcome of 63 consecutive games. Now we must consider how many possible outcomes there could be. Think of it like this: for every game, there are two possible winners. Since there are 63 games, we must multiply the number of possible winners for each game 63 times in a row. Algebraically, it would be 2 to the 63rd power. That gives us a total of 9,223,372,036,854,775,808 possibilities, or about 9.2 quintillion. Therefore, there is a 1 in 9.2 quintillion chance to pick the perfect bracket. Your probability of buying a winning Powerball ticket is much greater than your probability of a perfect bracket. In fact, you have a 1 in 292,201,338 chance of winning the Powerball jackpot.
It can be fun to make these kinds of connections in the classroom to challenge students and pique their interests. It can bring the world of math to the forefront of our everyday lives. Students begin to see the importance and relevance of math all around them. My goal is to continue to nurture the curiosity of these young learners.
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