Probability
Theoretical Probability
Theoretical probability is calculated using known facts about a situation, rather than by running trials. It uses the formula:
P(event) = Number of favourable outcomes ÷ Total number of possible outcomes
Probability Through Area
Probability can be pictured as a shaded fraction of a region. Draw every equally-likely outcome as one cell in a grid, shade the cells that count as “favourable,” and the probability is simply the shaded area divided by the total area — exactly the same fraction as favourable outcomes ÷ total outcomes.
The 10 marbles (4 red) become a grid of 10 equal cells, 4 shaded red:
4 of the 10 equal cells are shaded red, so P(red) = 4/10 = 2/5 — the shaded area is exactly 2/5 of the whole grid. This idea extends naturally to continuous regions too: for a point chosen completely at random inside a shape, P(landing in a region) = favourable area ÷ total area. For example, if a circular target of area 20 cm² sits inside a square dartboard of area 80 cm², the probability of a randomly thrown dart landing inside the circle is 20 ÷ 80 = 1/4, even though no counting of discrete outcomes is involved at all — only a ratio of areas.
Worked Example
A bag contains 10 marbles: 4 are red. P(red) = 4/10 = 2/5.
Theoretical probability assumes every outcome is equally likely — it's calculated, not measured.
Practice: Theoretical Probability
Calculate a theoretical probability or count favourable outcomes.