Probability of events, mutually exclusive and independent events, the addition and multiplication laws, conditional probability, and Venn and tree diagrams.

What this dot point is asking

Edexcel wants you to find probabilities of single and combined events, use the language of mutually exclusive and independent events, apply the addition and multiplication laws, calculate conditional probabilities, and use Venn diagrams and tree diagrams to model situations.

The answer

The laws of probability

Conditional probability

Diagrams

A Venn diagram shows each event as a region; the overlap is the intersection $A \cap B$ and the whole shaded area is the union $A \cup B$. A tree diagram lists outcomes in stages, with each branch labelled by its probability. You multiply along a path to find the probability of a sequence of outcomes, then add the relevant paths to combine several ways of reaching the same overall result.

Mutually exclusive and independent events

Complementary events

The complement of $A$, written $A'$, is the event that $A$ does not happen, and $P(A') = 1 - P(A)$. Using the complement is often the quickest route to an answer when the phrase "at least one" appears, because the complement of "at least one" is "none".

Examples in context

Try this

Q1. Events $A$ and $B$ satisfy $P(A) = 0.5$, $P(B) = 0.4$ and $P(A \cap B) = 0.2$. Find $P(A \cup B)$. [2 marks]

• Cue. $0.5 + 0.4 - 0.2 = 0.7$.

Q2. Using the values in Q1, find $P(A \mid B)$. [2 marks]

• Cue. $\dfrac{0.2}{0.4} = 0.5$, so $A$ and $B$ are independent.