I had a fascinating probability lesson with my year 11 class last week. I love probability partly because some of it is counter intuitive.
Hammond et al (1994). “Mathematics Learning for Life 3”, Oxford University Press, Melbourne. pp 78-80.
A lot of students were absent from school doing work placement. This prompted me to sit around some tables with all the students. I started by telling them that we were going to play a game that needed a six rolled on a standard die to start. Then I stated the essential question (yes, I have done INTEL training!):
“What is the most likely number of throws it would take before the first 6 appeared?”
Brodie said: “They all have the same chance sir, ‘cos like there is a one in six chance on any roll”.
“Well”, I said, “Lets do a few trials and see”.
Stewy rolled first and took 4 rolls to get a six. We drew a base scale and commenced a picture graph, using crosses. Shannon rolled next and took 3 rolls – an effort he was happy with. The die was passed to Kyra and she took 12 rolls to get a six! Brodie next – he got a six after 4 rolls.
“OK, lets each predict the best number if we say do 50 trials”.
Stewy quickly nominated 4 since it already had a head start. Shannon took 3, Kyra 2, and then Brodie 5. Stewy looked at me triumphantly and said “Ha, Ha, Mr T, you will have to have 1”.
I made a great show of complaining that it wasn’t fair. I dropped my lip and tried to look very depressed. I reluctantly agreed.
And so with Stewy grinning from ear to ear we began the experiment. We took turns to roll for a six, and Shannon kept the graph updated. The graph started to build with a few ohs and ahs when a 21 and a 26 was recorded. The numbers 3 and 4 easily took the lead. Stewy’s grin grew wider. And then it happened – three sixes in a row rolled on the first throw. A seven, twelve, another one, a nine, and then another six on the first roll. By the time we got to 50 trials, the number one was beating any other by at least 3 to 1.
Stewy was not happy when I informed him that I knew 1 was the best. I showed them the mathematics, which seemd to convince them that I was right.
We then started playing “Make a Moke” before the Assistant Principal’s voice over the PA summoned us to a school assembly!