Quick questions on Probability: addition and multiplication laws, conditional probability and diagrams - Edexcel A-Level Maths

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.

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".

The addition law subtracts $P(A \cap B)$ to avoid counting it twice.

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]

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