| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Complement and Difference Probabilities |
| Difficulty | Moderate -0.8 This is a straightforward Venn diagram problem requiring basic set theory and probability calculations. All parts involve routine application of standard techniques: drawing a Venn diagram from given percentages, finding complements, and calculating symmetric differences. No problem-solving insight or multi-step reasoning is needed, making it easier than average for A-level. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks |
|---|---|
| (a) Venn diagram with \(CD\) and \(PC\) circles showing regions: \(0.25\), \(0.45\), \(0.12\), \(0.18\) | B1 B1 B1 |
| (b) \(25\% + 18\% = 43\%\) | M1 A1 |
| (c) \(25\% + 12\% = 37\% = 0.37\) | M1 A1 |
**(a)** Venn diagram with $CD$ and $PC$ circles showing regions: $0.25$, $0.45$, $0.12$, $0.18$ | B1 B1 B1 |
**(b)** $25\% + 18\% = 43\%$ | M1 A1 |
**(c)** $25\% + 12\% = 37\% = 0.37$ | M1 A1 |
**Total marks: 7**
---70% of the households in a town have a CD player and 45% have both a CD player and a personal computer (PC). 18% have neither a CD player nor a PC.
\begin{enumerate}[label=(\alph*)]
\item Illustrate this information using a Venn diagram. [3 marks]
\item Find the percentage of the households that do not have a PC. [2 marks]
\item Find the probability that a household chosen at random has a CD player or a PC but not both. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q1 [7]}}