Ok, so, it is safe to say that the overwhelming majority of Math Misery? readers did not win at Powerball.
Now that our hopes and dreams of an early retirement have been dashed, it’s back to the grind. For those who teach, this is a great opportunity to give a follow up lesson on Powerball.
Natural lessons would be to discuss things like how much money was generated, how many unique combinations were probably played (actually quite tricky, but there is a mini-lesson in randomness as generated by humans and that generated by a good pseudo-random number generator (think back to the classical lesson about asking students to write down heads / tails coin flips vs recording actual coin flips)), how many people played, how many tickets did each person buy on average, how should the holder(s) of the winning ticket spend their money, and so forth.
But! Here at Math Misery? we try to go away from the run-of-the-mill. So, if you’re interested in mixing things up or otherwise incorporating a follow-up Powerball lesson with a twist on a familiar topic, here are a few ideas.
Patterns
One of the interesting things that will come up this week as the Powerball frenzy will start coming to a close is going to be all the near-miss stories. These will be stories about how someone missed the $1.5B jackpot by one number.
Are those people with near-misses more unlucky than a person who missed just as many numbers as a near-miss-er?
How can we mathematically define a near miss?
What if my ticket were the winning numbers times two modulo sixty? Is that a near miss?
Now, the winning power ball numbers were: 4 8 19 27 34 10.
What, if any, pattern can you find in the first five numbers?
This is a light question just to get students started. Pattern hunting and explaining is a good part of mathematics. The objective here is for students to find mathematical patterns, if possible and to explain them as such. An example is that the numbers as listed are [even, even, odd, odd, even] and including the red ball, it’s [even, even, odd, odd, even, even] and hey! That looks like a pattern — a pair of evens, followed by a pair of odds, followed by a pair of evens. Then from here, we can ask, what the likelihood is of seeing a pattern like this [even, even, odd, odd, even]?
If you somehow knew that the five number total of Powerball were going to be 92, how many tickets would you have to buy to guarantee that you get all sets of numbers adding to 92?
What if you also knew that the product and prime factorization of the product of the five numbers? How many tickets would you have to buy?
In other words, you are told that the winning numbers multiply as \(2^{6}\times3^{3}\times 17\times 19\). Now what? How many five number Powerball combinations would this information yield?
What if, combined with the information from the previous two questions, then how many tickets would we have to buy now? Does it mean more tickets or fewer tickets?
Hopefully you get the idea! Have some number fun with your students!