Today is rung 2 of 8 on this topic
Probability, sampling and why one survey isn't enough
Can do: Calculates simple and compound probabilities, and understands why sample size and selection matter.
Why it matters
Probability is where intuition is most reliably wrong, and sampling is how every statistic they'll ever be shown was produced.
What it looks like when it's wobbly
Believes in the gambler's fallacy โ that a coin is "due" โ and thinks a survey of their friends represents everyone.
โฑ๏ธ Two-minute check
"Five heads in a row. What's the chance of heads next? Why can't I survey this class to predict a national election?"
Solid looks like: Still one half, and a real point about biased or unrepresentative samples.
The full activity for this topic ยท 30 minutes
Run the Experiment
- 1Predict the theoretical probability first and write it down.
- 2Run ten trials and compare to the prediction โ it will look wrong.
- 3Run a hundred trials, pooling results with everyone in the house.
- 4Watch the experimental probability converge towards the theoretical one.
- 5Then discuss sampling: survey the house, then ask who's missing from that sample.
If it's too hard
One coin, tally to fifty.
If it's too easy
Compound events with a tree diagram, and with-versus-without replacement.
Say this
"The coin has no memory. Ten flips can look anything; a thousand can't."