This mini-lesson covers the Probability strand of OCR GCSE Maths (J560): the probability scale, sample space, relative & expected frequency, mutually exclusive and independent events, Venn diagrams, and the Higher-tier topics of tree diagrams and conditional probability.
Work through each screen, answer the questions as you go (most are calculations) and collect ⭐ stars. Press Start when you're ready.
A probability measures how likely an event is. It is always a number between 0 and 1 (which you can also write as a fraction, decimal or percentage):
A fair six-sided die is rolled. What is P(rolling an even number)?
Even numbers on the die: 2, 4, 6 → that is 3 successful outcomes.
Total outcomes = 6, so P(even) = 3/6 = 0.5
Key fact: the probabilities of all possible outcomes add up to 1. That means P(not A) = 1 − P(A).
Because all the probabilities of an experiment add to 1, the chance of an event not happening is whatever is left over:
The probability it rains tomorrow is P(rain) = 0.3.
P(no rain) = 1 − 0.3 = 0.7
Common slip: "not A" does not mean "half". It means everything else. If P(A) = 0.3, then P(not A) = 0.7, not 0.5.
The sample space is the set of all possible outcomes. Listing them (or drawing a two-way table) lets you count outcomes reliably:
One ball is taken at random. P(red) = 5/10 = 0.5; P(green) = 2/10 = 0.2.
P(not blue) = 1 − 3/10 = 7/10 = 0.7.
Tip: once you know the total (here 10), every single-pick probability is just "how many of that colour ÷ 10".
Two events are mutually exclusive if they cannot both happen at the same time — for example, rolling a 2 and rolling a 5 on a single die. For such events you can simply add the probabilities:
A spinner lands on red with probability 0.2 and on blue with probability 0.5. These can't both happen on one spin.
P(red or blue) = 0.2 + 0.5 = 0.7
Watch out: you can only add probabilities when the events are mutually exclusive. If events can overlap, adding double-counts the overlap — use a Venn diagram instead.
When outcomes are not equally likely (a biased spinner, a drawing pin), you estimate probability by experiment. This is the relative frequency:
Expected frequency works the other way: if you know a probability, expected number = P(event) × number of trials. E.g. P(red) = 0.2 over 50 spins gives 0.2 × 50 = 10 reds.
Two events are independent if one happening does not change the probability of the other — like two separate coin flips. To find the chance of both happening, multiply:
A fair coin is flipped twice. What is P(heads then heads)?
Each flip: P(heads) = 0.5, and the flips are independent.
P(H and H) = 0.5 × 0.5 = 0.25
Remember: "or" (mutually exclusive) means add; "and" (independent) means multiply. Mixing them up is the most common probability error.
Tap an event on the left, then its matching probability on the right. (The bag has 5 red, 3 blue and 2 green balls.)
When two events can overlap, a Venn diagram keeps the counts straight. Each region is counted exactly once:
Reading a Venn diagram: P(studies French) uses everyone inside the French circle = (8 + 5) ÷ 24 = 13/24. The overlap belongs to both circles.
A tree diagram shows the outcomes of two or more stages. You multiply along the branches, then add the results of the paths you want:
Higher only — dependent events: if the first outcome changes the second (e.g. balls taken without replacement), the probabilities on the second set of branches change. That is conditional probability.
A conditional probability is the chance of B given that A has already happened, written P(B | A). This matters when items are not replaced:
A bag has 5 red and 5 blue balls. Two are taken without replacement. P(both red)?
First red: 5/10. Now 4 red of 9 remain, so second red: 4/9.
P(both red) = 5/10 × 4/9 = 20/90 = 2/9
Higher only: tree diagrams for events without replacement and conditional probability are on the Higher tier of J560. The key is that the total and the counts drop by one after the first pick.
Sort each scenario by the rule you'd use. Mutually exclusive "or" events → add. Independent "and" events → multiply. Tap a card, then the box it belongs in.
The scale: every probability is between 0 (impossible) and 1 (certain); all outcomes add to 1.
Complement: P(not A) = 1 − P(A).
Sample space: list all outcomes; P = successes ÷ total.
Mutually exclusive ("or"): P(A or B) = P(A) + P(B) — add.
Independent ("and"): P(A and B) = P(A) × P(B) — multiply.
Frequency: relative frequency = successes ÷ trials; expected = P × trials.
Venn diagrams: handle overlapping events; count each region once.
Higher only: tree diagrams and conditional probability P(B | A) — for events without replacement.
You've covered the Probability strand of OCR GCSE Maths (J560) — Foundation content plus the Higher-tier tree diagrams and conditional probability. Press Finish to see your score.
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Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.