| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2021 |
| Session | November |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Mutually Exclusive Events Identification |
| Difficulty | Easy -1.2 This is a straightforward Venn diagram question requiring basic probability axioms (probabilities sum to 1) and recall of the definition of mutually exclusive events. Part (a) involves simple algebra to find p, and part (b) requires only identifying non-overlapping regions from the diagram—no problem-solving or conceptual depth required. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \([p = 1 - (0.2 + 0.2 + 0.1 + 0.2)] = \mathbf{0.3}\) | B1 (1) | B1 for \(0.3\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(A\) and \(C\) are mutually exclusive | B1 (1) | B1 for \(A\) and \(C\). Note: \(A \cap C\) or \(A \cap C = \varnothing\) is B0. If more than one case given they must all be correct e.g. \(A \cap B\) and \(C\) would be B0 |
## Question 1:
**Part (a)**
| Answer/Working | Marks | Guidance |
|---|---|---|
| $[p = 1 - (0.2 + 0.2 + 0.1 + 0.2)] = \mathbf{0.3}$ | B1 (1) | B1 for $0.3$ |
**Part (b)**
| Answer/Working | Marks | Guidance |
|---|---|---|
| $A$ and $C$ are mutually exclusive | B1 (1) | B1 for $A$ and $C$. Note: $A \cap C$ or $A \cap C = \varnothing$ is B0. If more than one case given they must **all** be correct e.g. $A \cap B$ and $C$ would be B0 |
---1.\\
\includegraphics[max width=\textwidth, alt={}, center]{6dfefd72-338f-40be-ac37-aef56bfaccaa-02_399_743_248_662}
The Venn diagram, where $p$ is a probability, shows the 3 events $A , B$ and $C$ with their associated probabilities.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $p$.
\item Write down a pair of mutually exclusive events from $A , B$ and $C$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 2 2021 Q1 [2]}}