Conditional Probability (Cambridge (CIE) IGCSE International Maths: Extended): Revision Note

Conditional probability can be written using formal notation.

The notation $\mathrm{P}\left(A|B\right)$ describes the probability of event A occurring, given that event B has already occurred.

Note that you are not expected to know this notation for the exam, but you are expected to be able to calculate conditional probabilities using Venn diagrams, tree diagrams or tables.

• Look out for conditional probability questions within larger questions on two-way tables, Venn diagrams or tree diagrams

  • They often use the phrase given that

A Venn diagram is shown below.

$$\begin{gathered} A=\left\{2,6,12,14,28\right\} \\ B=\left\{7,14,21,28,35\right\} \\ \xi =\left\{1,2,5,6,7,12,14,21,28,35\right\} \end{gathered}$$

A number is picked at random.

Find the probability that the number is in set $A$ given that it is in set $B$.

Answer:

Given that B has already happened, your probability will be out of number of numbers in B

Out of the 5 numbers in B, 2 of them are in A

Write as a fraction

$\frac{2}{5}$