1 / 15
Session 5 of 8
Probability
& Prediction
Why does getting 8 heads in 10 flips NOT mean your coin is broken? Today we find out.
🔍 Data Science for Young Minds · Grade 5 — Data Detective
2 / 15
Today's Plan
What We're Doing Today
- 🎯 Hook — 8 heads in 10 flips: broken coin or normal randomness?
- 📊 Experimental vs. theoretical probability
- 🔢 Calculating probability as a fraction, decimal, and %
- 🪙 Coin flip experiment — 10 flips vs. 50 flips
- 📈 Law of Large Numbers — why more trials = more reliable
- 🔬 Where simulations are used in real science
3 / 15
Opening Hook
Is This Coin Broken?
Before class, your teacher flipped a coin 10 times and got 8 heads and 2 tails.
Is this coin broken — or is this normal? Vote now.
- Option A: The coin is biased — heads comes up too often
- Option B: This is normal randomness — it can happen with a fair coin
- Option C: I'm not sure — I need more information
By the end of today, you'll know the answer — and be able to explain it with math.
4 / 15
Lesson 1
What Is Probability?
Probability is the likelihood that a specific outcome will occur. It's always between 0 (impossible) and 1 (certain).
0 — Impossible0.5 — 50/501 — Certain
P(heads) = 1/2 = 0.5 = 50%
One heads outcome out of two possible outcomes
P(rolling a 6) = 1/6 ≈ 17%
One favorable outcome out of six possible outcomes
P(rain tomorrow) = 0.7 = 70%
Based on historical patterns — not guaranteed!
P(impossible event) = 0
Rolling a 7 on a standard 6-sided die
5 / 15
Lesson 2
Experimental vs. Theoretical
🔬 Theoretical Probability
- What should happen mathematically
- Based on equally likely outcomes
- P(heads) = 1/2 = 50% — always, for a fair coin
- Doesn't change regardless of past flips
🪙 Experimental Probability
- What actually happened in your trials
- Based on data you collect
- 8 heads in 10 flips = 80% experimental
- Changes with every experiment
They can be very different — especially with small numbers of trials. Over many trials, experimental probability converges toward theoretical.
6 / 15
Lesson 2
Why 8 Heads Is NOT Surprising
With only 10 flips, there's a reasonable chance of getting 8 heads — even with a perfectly fair coin.
10
Flips
Getting 8 heads is unusual but completely possible. Wide variation expected.
50
Flips
Most results will be between 40–60% heads. Getting 80% would be suspicious.
1000
Flips
Results will be very close to 50%. Getting 80% here would be extremely strong evidence of a biased coin.
Answer to the hook: 8/10 heads is normal randomness with a fair coin. It does NOT prove bias. You need many more trials to draw that conclusion.
7 / 15
Activity Time!
Coin Flip Experiment
You're going to collect your own probability data — and see the Law of Large Numbers in action.
- 🪙 Round 1: Flip your coin 10 times. Tally H and T. Calculate % heads.
- 📊 Record: # heads ÷ 10 × 100 = ____% (your experimental probability)
- 🪙 Round 2: Flip your coin 50 times (flip in groups of 10). Tally. Calculate % heads.
- 📊 Record: # heads ÷ 50 × 100 = ____% (your experimental probability)
- 📈 Graph: Draw bars for your 10-flip %, 50-flip %, and the theoretical 50%.
⏱ You have 20 minutes. Work carefully — every flip counts!
8 / 15
🧠
Brain Break — Probable or Improbable?
Stand for PROBABLE (more than 50% likely), sit for IMPROBABLE (less than 50% likely).
"It will rain somewhere in the world today" · "You will roll a 6 on your first try" · "A flipped coin lands on heads" · "You draw a red card from a standard deck" · "It snows in July in Florida"
Probability is about the whole range — from impossible to certain!
9 / 15
Debrief
What Did Your Data Show?
"How close was your 10-flip result to 50%? How about your 50-flip result? Who had the most unusual result in 10 flips?"
- Who got the highest % heads in their 10-flip round? The lowest?
- How much variation was there across the class for 10 flips vs. 50 flips?
- When we combine all class flips — how close is the total to 50%?
- What would the graph look like if we all did 200 flips?
10 / 15
Lesson 3
The Law of Large Numbers
As the number of trials increases, the experimental probability gets closer and closer to the theoretical probability.
What it means:
- Small sample: lots of random noise
- Large sample: noise averages out
- This is why science uses large sample sizes
- This is why casinos always win in the long run
What it does NOT mean:
- After 5 tails, heads is NOT "due"
- Each flip is independent — history doesn't matter
- The "gambler's fallacy" says past flips predict future — they don't
- More trials = more reliable — but never perfectly certain
11 / 15
Lesson 3
Simulations in Real Science
Scientists use simulations — models that imitate probability — when real experiments are impossible, expensive, or unethical.
- 💊 Drug testing: Simulate millions of patients before human trials begin
- 🌪️ Weather forecasting: Run thousands of simulated atmospheres to predict probability of rain
- 🚗 Crash testing: Computer simulations before any physical crash test
- 💹 Economics: Simulate market conditions to predict recession probability
- 🧬 Genetics: Simulate DNA combinations across generations
Your coin flip experiment today was a simulation — a physical model of a 50/50 random process. Real scientists do the same thing, just with computers and millions of "flips."
12 / 15
Lesson 3
Probability and Data Literacy
- 📰 "Study shows 30% of people experience side effects" — was this 10 people or 10,000? Sample size matters.
- 🎰 "This slot machine pays out 1 in 20 times" — over many trials, the house still wins because the payout is less than the odds.
- 🌦️ "70% chance of rain" — doesn't mean it will definitely rain. It means in similar conditions, it rained 70% of the time historically.
- 🏥 "You have a 1% chance of complications" — with 10,000 patients, that's 100 people. Small % can mean large absolute numbers.
A Data Detective always asks: "How many trials? What's the sample size? Is this experimental or theoretical?"
13 / 15
Analysis Time
Written Analysis
"Compare your 10-flip and 50-flip results. Which was closer to 50%? Use your actual percentages to explain. What would happen with 200 flips?"
✍️ 5 minutes. Use your worksheet — Part 4. Cite your actual numbers. Connect to the Law of Large Numbers.
14 / 15
Vocabulary Check
Session 5 Key Terms
Probability
Likelihood of an outcome; expressed as fraction, decimal, or %
Experimental Probability
What actually happened in your trials
Theoretical Probability
What should happen mathematically with a fair process
Trial
One instance of an experiment (one coin flip)
Law of Large Numbers
More trials → experimental probability approaches theoretical
Simulation
A model used to imitate a random process and collect probability data
15 / 15
Session Close
The Probability Detective Rule
"A single unexpected result isn't evidence of anything.
Only many trials reveal the truth."
- ✅ You can calculate experimental and theoretical probability
- ✅ You understand why small samples produce variable results
- ✅ You've demonstrated the Law of Large Numbers with real data
- ✅ You can explain why 8 heads in 10 flips is completely normal
Next session: Two things can happen at the same time without one causing the other. We investigate correlation vs. causation — and some very funny examples.