2.4StatisticsStretch

Probability Formulae

Two formulae handle most probability problems: the addition formula for “or”, and the multiplication form of the conditional probability formula for “and”. Together they let you compute combined probabilities.

24 min Video by Zeeshan Zamurred Conditional Probability

Edexcel A level Maths: 2.4 Probability Formulae (Addition and Conditional)Watch the full walkthrough before the notes below.

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What you'll be able to do

Use the addition formula
Use the multiplication formula
Rearrange the conditional formula
Apply to combined events

Addition formula

For any two events, $P (A \cup B) = P (A) + P (B) - P (A \cap B)$ . Subtracting the overlap avoids double-counting.

P (A \cup B) = P (A) + P (B) - P (A \cap B)

Addition (“or”) formula.

Multiplication formula

Rearranging the conditional formula gives $P (A \cap B) = P (B) P (A ∣ B)$ — useful for finding the probability of both events.

P (A \cap B) = P (B) P (A ∣ B)

Multiplication (“and”) formula.

0.5 + 0.4 - 0.2

= 0.7

Answer

0.7

Tip — For mutually exclusive events P(A∩B) = 0, so P(A∪B) = P(A) + P(B).

Formula recap

P (A \cup B) = P (A) + P (B) - P (A \cap B)

Addition.

P (A \cap B) = P (B) P (A ∣ B)

Multiplication.

Common mistakes to avoid

Forgetting to subtract the overlap in the addition formula.

Subtract P(A∩B) to avoid double-counting.

Using P(A)P(B) for P(A∩B) when events are not independent.

Use P(B)P(A | B) in general.

Key takeaways

P(A∪B) = P(A) + P(B) − P(A∩B).
P(A∩B) = P(B)P(A | B).
Mutually exclusive: P(A∩B) = 0.

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