Probability

Season 04

Episode 08

Duration 23:13

✓ Link copied to clipboard

Every coin toss, every roll of a die, every drop of rain in the forecast: the world runs on chances, and mathematics has a way to count them. In this episode of Bill Nye the Science Guy, Bill shows how probability lets you predict how often something will happen, even when you cannot say exactly when.

In this episode you will discover:

What we mean by a one in two chance and why heads and tails average out over many tosses
How independent events like coin flips have no memory of what came before
Why seven is the most likely number when you roll two dice
How X and Y chromosomes make the chance of a boy or a girl very close to one in two
Why the odds of winning a state lottery are around one in five million
How scientists use samples of clovers or banded birds to make predictions

How to think in probabilities

Bill’s central idea is that probability does not tell you what will happen next, it tells you what will happen on average over many, many tries. A tossed coin might land tails nineteen times out of the first twenty flips and still average out to fifty fifty over a few hundred, because each new flip is independent of the last. That same way of thinking lets insurance companies price a policy, lets weather forecasters give a percentage chance of rain and lets biologists explain why families end up with roughly half boys and half girls.

Key concept
Probability
A number between zero and one that says how often an outcome is expected among all the ways things could turn out.

Key concept
Large numbers
Short runs of heads or tails look lucky, but over many trials the results settle down to the expected proportions.

Key concept
Independent events
One coin flip or dice roll does not affect the next, so a run of tails does not make heads more likely to follow.

Bill Nye’s demonstrations

Bill fires up the Flipmaster 50/50, a giant coin flipping machine, and lets the tally run until heads and tails settle close to even after dozens of tosses. He shows a gumball machine with forty blues, twenty greens and ten each of the other colours and predicts, correctly, that the next gumball is most likely to be blue. To show truly long odds he opens a box packed with five million polystyrene chips, one of them red, and tries to fish out the red one, which is the same as the odds on a state lottery. He then loads up the dice slinging catapult of science to demonstrate why a seven is the most likely roll of two dice, and rounds off in a clover patch to work out the probability of finding a four leaf clover in a roped off ten square metre plot.

Try this at home

The coin tally test. Flip a coin one hundred times and keep a running tally in two columns. Early on the score will bounce around in surprising streaks, but by the time you finish the two columns are almost always very close to fifty each. That is the law of large numbers, doing exactly what Bill’s Flipmaster shows.

The two dice test. Roll a pair of dice thirty six times and tally the sum from two to twelve. Seven will nearly always come up most often, because there are six different ways to make it (one plus six, two plus five, three plus four, and so on), and only one way to make two or twelve. That is why casinos and board games treat seven the way they do.

Cool facts

With two dice there are six ways to make a seven, more than any other total, so it turns up about one time in six.
In a room of just twenty three people, the chance that two of them share a birthday is about one in two.
Your chance of winning a typical state lottery is around one in five million.
Whether a baby is a boy or a girl comes down to a fifty fifty chance of an X or a Y chromosome from the father.

Science update: since this episode aired

Weather forecasting has been transformed by machine learning. In late 2024 Google DeepMind published GenCast, a diffusion model that outperformed the European ensemble on ninety seven per cent of tested targets and produced a fifteen day probabilistic forecast on a single chip in about eight minutes. Nature, Price et al. 2024
Hurricane track prediction, which is Bill’s classic weather example, keeps improving. The National Hurricane Center reports that in 2024 official Atlantic track forecasts were the most accurate on record at every time interval from twelve to one hundred and twenty hours ahead. NOAA National Hurricane Center Verification Report
Probability has moved deep into medicine. Doctors can now combine a person’s genome with clinical measurements to work out a polygenic risk score, and a 2024 UK study of forty four thousand NHS Health Check patients showed that adding this score to standard risk models flagged more people at high risk of cardiovascular disease. European Heart Journal, Samani et al. 2024

🎓

Curriculum focus

Built on NGSS MS-LS3-2 and HS-LS3-3 (using probability to explain the variation of inherited traits). Complementing that, it is pitched at KS3 mathematics (probability, likely outcomes and relative frequency) and works as an introduction or revision aid for GCSE and IGCSE mathematics on probability trees and mutually exclusive events, and for GCSE biology on inheritance and sex determination, across boards such as AQA, Edexcel, OCR and Cambridge IGCSE. The worksheet and critical thinking questions take these ideas further than the episode alone.

NGSS MS-LS3
KS3 maths
GCSE revision
IGCSE revision
Probability
Inheritance

Interactive Science Lesson

Probability

Based on Bill Nye the Science Guy · Season 4, Episode 8 · 23 min

The future is a mystery, right? Not exactly! While we might not be able to predict what will happen in one specific moment, by using the mathematics of Probability, we can actually predict how things will behave over time. Let us decode the odds!

Step 1 of 6 · Engage

Engage

Predicting the Unpredictable!

Explore

Put Your Instincts to the Test

Think about how random chance really works in the real world. Pick an answer for each scenario, then see if your mathematical instincts were right.

1. If you flip a perfectly normal coin and get "Heads" five times in a row, what is the probability that the *next* flip will be "Tails"?

2. If you are in a room with just 23 people, what are the odds that two people in that room share the exact same birthday?

Explain

Understanding the Science

Tap each card to uncover the mathematical rules and scientific concepts that govern chance, luck, and probability in the natural world.

Key Concepts

Interactive: The Galton Board Simulator

Bill Nye the Science Guy used a giant machine dropping balls through a maze of pegs to prove how random chance creates patterns. You try it! Drop balls through the peg board. At every peg, the ball has an exact 50/50 chance of bouncing left or right. Watch as pure randomness naturally builds a perfectly predictable, symmetrical Bell Curve at the bottom!

DISTRIBUTION DATA

Total Balls: 0

Shape Analysis:
Awaiting Data...

Elaborate

Apply Your Knowledge

Let us see if you can correctly identify the essential mathematical terminology associated with probability and statistics.

Match the Concepts

Click a mathematical term to select it, then click the matching description to place it.

Probability Terminology

The mathematical chance that a specific event will happen, usually expressed as a fraction or percentage.

The different ways variables can be mixed together, like the 6 different ways two dice can add up to a 7.

A common shape on a graph that happens when purely random events naturally pile up around the average.

Extremely rare events that fall way outside the normal average, like winning the lottery.

Real-World Challenge

Imagine you are looking at a gumball machine filled with exactly 100 gumballs. 50 are blue, 40 are red, and 10 are yellow. You really want a blue gumball. Since blue has the absolute highest probability of coming out, why can you not *guarantee* that the first coin you put in will give you a blue gumball?

Science Update

What Has Changed Since This Episode Aired

This episode originally aired in 1996. Since then, the mathematical science of probability and computing power has exploded into a whole new era!

Evaluate

Test Your Understanding

Answer these 10 questions and get instant feedback. How many can you get right?

Reflection

Think about a choice you made today. What was the probability that you would make that specific choice instead of another one? How do the concepts of random chance and mathematical averages affect your daily life?

.ss-reveal__body { display: block !important; } .ss-predict__reveal { display: block !important; } .ss-concept-card__body { display: block !important; } .ss-progress { display: none !important; } .ss-nav-row { display: none !important; } [data-ss-quiz-q] { display: block !important; } .ss-quiz__display { display: none !important; }

Probability

How to think in probabilities

Bill Nye’s demonstrations

Try this at home

Bill Nye The Science Guy

Season 1 (20 episodes)

Season 2 (20 episodes)

Season 3 (20 episodes)

Season 4 (20 episodes)

Season 5 (20 episodes)

Episode Discussion

Join the Discussion Cancel Reply

Probability

Predicting the Unpredictable!

Put Your Instincts to the Test

Understanding the Science

Key Concepts

Probability

50/50 Odds

Combinations

The Bell Curve

The Average

Outliers

Genetics

Risk Assessment

Interactive: The Galton Board Simulator

Apply Your Knowledge

Match the Concepts

Real-World Challenge

What Has Changed Since This Episode Aired

Test Your Understanding

Results

Reflection