P1ProbabilityFoundation

Basic Probability

Probability measures how likely something is, on a scale from 0 (impossible) to 1 (certain). Most of GCSE probability is built on one simple idea: favourable outcomes over total outcomes.

30 min AQA GCSE Maths

What you'll learn

Use the 0 to 1 probability scale
Calculate the probability of a single event
Use that probabilities sum to 1
Find expected frequency

The probability of an event

For equally likely outcomes, the probability is the number of ways it can happen divided by the total number of outcomes. Probabilities are written as fractions, decimals or percentages between 0 and 1.

P (event) = \frac{favourable outcomes}{total outcomes}

The basic probability formula.

1Favourable = 3 reds; total = 8 balls.

P (red) = \frac{3}{8}

Answer

\frac{3}{8}

Totals and expected frequency

The probabilities of all outcomes add up to 1, so $P (not A) = 1 - P (A)$ . $Expected frequency$ = probability × number of trials.

Tip — A probability can never be more than 1 or less than 0 — if you get 1.5, check your working.

Remember these

P = \frac{favourable}{total}

Probability of an event.

P (not A) = 1 - P (A)

Complement.

expected = P \times trials

Expected frequency.

Watch out for these

Giving a probability bigger than 1.

All probabilities are between 0 and 1.

Forgetting that all outcomes sum to 1.

Use P(not A) = 1 − P(A).

Key takeaways

Probability scale runs 0 (impossible) to 1 (certain).
P = favourable ÷ total outcomes.
All probabilities sum to 1; expected = P × trials.

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