🎪 Sample City & The Probability Carnival

Survey the city, beat the games — where good samples and honest odds win the big prizes.

REMEMBER: A random sample gives every member an equal chance — that's what makes a small sample trustworthy. Probability always lives between 0 and 1. For compound events, list the whole sample space (a table or tree helps) — and multiply along the branches, don't add.

Part 1 · Sample City

All 100 residents secretly prefer either 🟢 veggie or 🟡 pepperoni pizza. You can't ask everyone — so survey a random 10 and estimate the whole city! Survey several times to watch estimates wobble... then try the BAD sample and see what bias does.

Part 2 · The Carnival Games

Step right up! Each booth offers a game of chance. Predict the probability of winning and lock it in — then the booth opens its sample space and shows every possible outcome. Afterward, run 200 quick plays and see how close real results come to the theory!

Correct predictions: 0

Part 3 · Behind the Booths

Three machines run this carnival. Feed them your numbers — each prints every step and the why.

You surveyed a random sample. Scale it up to estimate the whole population.

Two teams, five quiz scores each. The machine compares their CENTER (mean) and SPREAD (range) — and says what each one means.

Pick a two-step experiment. The builder counts the steps, lists EVERY outcome, and finds the target probability — multiplying, never adding.

Part 4 · Grand Prize Quiz

Question 1 of 10 Score: 0

📗 Word Box

Population
The ENTIRE group you want to know about — every resident, every student, every part in the shipment.
Random sample
A smaller group chosen so every member of the population has an equal chance of being picked. Small but trustworthy.
Biased sample
A sample that favors some members over others — like surveying one street or only your friends. Its results mislead.
Inference
Using a sample's results to estimate the whole population. Different samples give slightly different — but reasonable — estimates.
Probability
A number from 0 (impossible) to 1 (certain) measuring how likely something is. Nothing can be more certain than certain!
Sample space
The list of EVERY possible outcome of an experiment. For two coins: HH, HT, TH, TT — all four, not three!
Compound event
An event built from two or more steps, like a spin AND a flip. Multiply the chances along the way.
Simulation
Running an experiment many times (often by computer) to see how often something happens. More trials → closer to theory.
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