| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2024 |
| Session | October |
| Paper | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Three-Set Venn Diagram Construction |
| Difficulty | Moderate -0.8 This is a straightforward Venn diagram question requiring basic set theory and probability calculations. Students are given most values directly and only need to find one missing value (the intersection of all three sets) using the total of 200, then perform simple probability calculations including conditional probability. This is standard S1 material with no novel problem-solving required. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| (a) [Venn diagram with three overlapping circles] | B3 | For a fully correct Venn diagram |
| (B2 for at least 6 numbers in the correct place on the Venn diagram) | ||
| (B1 for at least 3 numbers in the correct place on the Venn diagram) | ||
| Treat blanks on the diagram as zero | ||
| Condone correct probabilities instead of frequencies e.g. \(\frac{22}{200}\) oe or 0.11 as 22 | ||
| (b)(i) \(\frac{\text{'14'}}{200}\) | B1ft | For \(\frac{\text{'14'}}{200}\) oe if their Venn diagram |
| (b)(ii) \(\frac{\text{'33'+}'11'\text{+'42'+}'32'}{200}\) \(\frac{118}{200}\) | M1 A1 | \(\frac{200 - \text{'29'}-\text{'22'}-\text{'14'}-\text{'17'}}{200}\) \(\frac{118}{200}\) ft their Venn diagram. May be implied |
| by \(\frac{118}{200}\) oe | ||
| (c) \(\frac{\text{'14'+}'11'+}'22'\text{+}'33'}{...}\) = \(\frac{n}{80}\) provided the answer gives a probability and \(0 < n < 80\) ft the Venn diagram for numerator \(\frac{\text{'14'+}'11'}{\text{'14'+}'11'+}'22'\text{+}'33'} = \frac{\text{'n'}}{80}\) provided \(0 < n < 80\) ft the Venn diagram for numerator | M1 | For a correct ratio in terms of \(n\) e.g. \(\frac{2n+1}{2n}\) oe ft their Venn diagram for the denominator |
| or \(\frac{\text{'m'}}{0.4}\) where \(0 < m < 0.4\) ft the Venn diagram for numerator | ||
| \(\frac{25}{80}\) | A1 | For \(\frac{25}{80}\) oe Allow 0.313 |
**(a)** [Venn diagram with three overlapping circles] | B3 | For a fully correct Venn diagram
| | (B2 for at least 6 numbers in the correct place on the Venn diagram)
| | (B1 for at least 3 numbers in the correct place on the Venn diagram)
| | Treat blanks on the diagram as zero
| | Condone correct probabilities instead of frequencies e.g. $\frac{22}{200}$ oe or 0.11 as 22
**(b)(i)** $\frac{\text{'14'}}{200}$ | B1ft | For $\frac{\text{'14'}}{200}$ oe if their Venn diagram
**(b)(ii)** $\frac{\text{'33'+}'11'\text{+'42'+}'32'}{200}$ $\frac{118}{200}$ | M1 A1 | $\frac{200 - \text{'29'}-\text{'22'}-\text{'14'}-\text{'17'}}{200}$ $\frac{118}{200}$ ft their Venn diagram. May be implied
| | by $\frac{118}{200}$ oe
**(c)** $\frac{\text{'14'+}'11'+}'22'\text{+}'33'}{...}$ = $\frac{n}{80}$ provided the answer gives a probability and $0 < n < 80$ ft the Venn diagram for numerator $\frac{\text{'14'+}'11'}{\text{'14'+}'11'+}'22'\text{+}'33'} = \frac{\text{'n'}}{80}$ provided $0 < n < 80$ ft the Venn diagram for numerator | M1 | For a correct ratio in terms of $n$ e.g. $\frac{2n+1}{2n}$ oe ft their Venn diagram for the denominator
| | or $\frac{\text{'m'}}{0.4}$ where $0 < m < 0.4$ ft the Venn diagram for numerator
$\frac{25}{80}$ | A1 | For $\frac{25}{80}$ oe Allow 0.313
**Total: 8 marks**\begin{enumerate}
\item A group of 200 adults were asked whether they read cooking magazines, travel magazines or sport magazines.\\
Their replies showed that
\end{enumerate}
\begin{itemize}
\item 29 read only cooking magazines
\item 33 read only travel magazines
\item 42 read only sport magazines
\item 17 read cooking magazines and sport magazines but not travel magazines
\item 11 read travel magazines and sport magazines but not cooking magazines
\item 22 read cooking magazines and travel magazines but not sport magazines
\item 32 do not read cooking magazines, travel magazines or sport magazines\\
(a) Using this information, complete the Venn diagram on page 11
\end{itemize}
One of these adults was chosen at random.\\
(b) Find the probability that this adult,\\
(i) reads cooking magazines and travel magazines and sport magazines,\\
(ii) does not read cooking magazines.
Given that this adult reads travel magazines,\\
(c) find the probability that this adult also reads sport magazines.
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{fe416f2e-bc81-444b-a0ca-f0eae9a8b149-11_851_1086_296_493}
\end{center}
\hfill \mbox{\textit{Edexcel S1 2024 Q3}}