Probability: an interactive probability course
Probability is an interactive probability course that starts with the chance of rolling a 4 and ends with the binomial and normal distributions. Its 36 short sections cover sample spaces, experimental probability, complements, the OR and AND rules, Venn and tree diagrams, independent and dependent events, conditional probability and expected value, with a simulator or practice question in most of them.
It is built for school and early university students, and for adults who want to reason clearly about chance, risk and games.
What the probability course covers
| Sections | Topic | What you do |
|---|---|---|
| 1 to 4 | What probability is, fractions and the 0 to 1 scale | Drag events onto a probability line, then find the chance of drawing a colour from a bag |
| 5 to 7 | Sample spaces and listing outcomes | Fill a coin by die outcome grid and pick out an event |
| 8 to 10 | Theoretical and experimental probability | Flip a simulated coin many times and estimate probabilities from data |
| 11 to 13 | Complementary events | Use P(not A) = 1 − P(A) as a shortcut |
| 14 to 17 | The OR and AND rules, and Venn diagrams | Build a Venn diagram and read off P(A or B) and P(A and B) |
| 18 to 20 | Tree diagrams | Click paths on a tree and multiply along them |
| 21 to 23 | Independent and dependent events | Draw marbles with and without replacement, then classify events |
| 24 to 26 | Conditional probability | Edit a two-way table and work out conditional probabilities |
| 27 to 29 | Expected value | Play a dice game and watch your average winnings settle on the expected value |
| 30 to 33 | Probability distributions and the binomial distribution | Change n and p and watch the histogram reshape, then use the binomial formula |
| 34 to 36 | The normal distribution | Reshape a bell curve and use the 68, 95, 99.7 rule |
The foundations
The first third makes sure the basics are solid: probability as favourable outcomes over total outcomes, the same chance written as a fraction, decimal or percentage, and listing every outcome so none are missed. A coin simulator shows the law of large numbers: the more you flip, the closer the share of heads gets to 0.5.
Combining events
The middle sections cover the rules most exam questions test. You add for OR, subtracting any overlap, and multiply for AND when events are independent. Venn diagrams and tree diagrams make both rules visual, and drawing marbles without replacement shows how a first pick changes the second. Conditional probability then narrows the sample space to what you already know.
Expected value and distributions
The last part asks what happens on average. A game that costs £2 and pays £10 for a six has an expected value of 10 × 1/6 − 2, a loss of about 33p a game, so it is not worth playing in the long run. The course then introduces distributions, the binomial formula for counting successes, and the normal curve with its 68, 95 and 99.7 percent bands.
Try a question from the course
When every outcome is equally likely, the probability is the number of outcomes you want divided by the total. A bag holds 4 red, 6 blue and 2 yellow marbles, 12 in all. The chance of picking red is 4/12, which simplifies to 1/3.
Now try one with a new bag. Type the probability as a fraction and press Mark to check it in the course.
Type the probability of drawing a colour from a bag of marbles as a fraction.
Press Mark to have your answer marked in the Probability course.
Who this course is for
- School students meeting probability for the first time, or revising tree diagrams, Venn diagrams and conditional probability for an exam.
- Students starting statistics, who need the binomial and normal distributions explained from the ground up.
- Adults who want to think more clearly about odds, risk and whether a game or bet is fair.
What you need to know first
Fractions, decimals and percentages, and how to multiply and simplify fractions. That is enough for the first two thirds. The binomial formula uses powers and a counting term that the course explains, so the Algebra course helps if formulas with letters are new.
How long it takes
There are 36 sections and most take a few minutes: a short explanation, then a simulator, a diagram or a practice question. Learners without a plan can open two sections of a course a day, in order, which takes 18 days. A plan removes the daily limit and lets you jump straight to any topic, such as conditional probability or the normal distribution.
Common questions
Is this probability course free?
What topics does a probability course cover?
Is probability hard to learn?
What is the difference between independent and dependent events?
Does it cover statistics too?
Do I need a calculator?
Revision cards
Say the answer first, then flip the card to check it.
Where to go next
- Solve it
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