# Who’s luckier?

Lesson here.

So today I asked my Year 12 Maths Studies students if they have ever bought a Mars Bar during the “Free Bars” Promotion where 1 in every 6 bars wins a free Mars Bar. A few hands around the classroom went up and we were discussing who had the longest run of free bars..

I had already spent the morning reading about different bloggers’ stories of success, failure, and claims that the Illuminati have been messing with the packets.

I took a few screenshots of some random stories and then used them to pose a question that caused much debate,

If one person buys wins 4 free bars in a row, and a different person wins 8 free bars from a total of 10, who was luckier?

I did this by showing them two separate stories via screenshots. The class was divided into four table groups. They were asked to first write down their “gut feeling” without overthinking, doing any calculations, or talking to anyone. Then, they discussed their thoughts amongst their peers.

3 groups felt that 4 out of 4 was much luckier than 8 out of 10.

I then introduced Binomial Distributions.

Who do you think was more lucky?

After exploring, debating, questioning, and calculating, they found the correct answer and, most importantly, the importance of the Maths they had just learnt.

When they thought that they had it all figured out, I knew it was just the right time to drop scenario 2 on them with another screenshot of a blogger’s story;

A third person buys a whole box of Mars Bars (36 bars) and claims that the whole promotion is a scam. Only 1 of the 36 Mars Bars was a Free Bar.

I then asked them, in table groups, to come up with the best solution to test whether it was a scam or not. I’ll admit, it was a Friday afternoon, so my students’ minds weren’t operating any where near their usual levels. Three of the four groups felt that, “buying a few more boxes,” would be the best and most efficient solution.

Do you agree with my students?

I then introduced Hypothesis Testing for Binomial Probabilities.

I taught them about the likeliness it has with Hypothesis Testing for Population Means of Normal Distributions and, before too long, they made sense of their answer and understood the importance of the Maths they had just learnt.

Twice in 45 minutes.