| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2021 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Venn diagram with three events |
| Difficulty | Moderate -0.8 This is a straightforward Venn diagram question requiring basic probability operations: reading values from the diagram, adding probabilities for unions, and applying the conditional probability formula P(A|B') = P(A∩B')/P(B'). All values are given explicitly in the diagram, requiring only careful arithmetic with no conceptual challenges or problem-solving insight. |
| 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 |
|---|---|---|
| \([0.15 + 0.13 + 0.12 =]\ \mathbf{0.4}\) | B1 (1 mark) | For 0.4 or exact equivalent |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.15 + 0.20 + 0.23 + 0.12\) or \(1-(0.17+0.13)\) or \(0.35+0.35 = \mathbf{0.7}\) | M1, A1 (2 marks) | M1 for a correct sum or expression; A1 for 0.7 or exact equivalent, correct answer with no incorrect working 2/2 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\left[P(A \mid B') =\right] \frac{P(A \cap B')}{P(B')}\) and \(\frac{p}{\text{"0.4"}}\) or \(\frac{0.15}{\text{"0.4"}}\) | M1 | M1 for \(\frac{P(A \cap B')}{P(B')}\) and \(\frac{p}{\text{"0.4"}}\) where \(0 < p <\) "0.4", or just \(\frac{0.15}{\text{"0.4"}}\); condone one missing "P" |
| \(= \frac{3}{8}\) | A1 (2 marks) | A1 for \(\frac{3}{8}\) or exact equivalent e.g. 0.375; \(\frac{0.15}{0.4}\) is A0; correct answer with no incorrect working 2/2 |
## Question 1:
### Part (a)
$[0.15 + 0.13 + 0.12 =]\ \mathbf{0.4}$ | B1 (1 mark) | For 0.4 or exact equivalent
### Part (b)
$0.15 + 0.20 + 0.23 + 0.12$ or $1-(0.17+0.13)$ or $0.35+0.35 = \mathbf{0.7}$ | M1, A1 (2 marks) | M1 for a correct sum or expression; A1 for 0.7 or exact equivalent, correct answer with no incorrect working 2/2
### Part (c)
$\left[P(A \mid B') =\right] \frac{P(A \cap B')}{P(B')}$ and $\frac{p}{\text{"0.4"}}$ or $\frac{0.15}{\text{"0.4"}}$ | M1 | M1 for $\frac{P(A \cap B')}{P(B')}$ **and** $\frac{p}{\text{"0.4"}}$ where $0 < p <$ "0.4", or just $\frac{0.15}{\text{"0.4"}}$; condone one missing "P"
$= \frac{3}{8}$ | A1 (2 marks) | A1 for $\frac{3}{8}$ or exact equivalent e.g. 0.375; $\frac{0.15}{0.4}$ is A0; correct answer with no incorrect working 2/2
---\begin{enumerate}
\item The Venn diagram shows the events $A , B$ and $C$ and their associated probabilities.\\
\includegraphics[max width=\textwidth, alt={}, center]{4f034b9a-94c8-42f2-bd77-9adec277aba6-02_584_1061_296_445}
\end{enumerate}
Find\\
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { P } \left( B ^ { \prime } \right)$
\item $\mathrm { P } ( A \cup C )$
\item $\mathrm { P } \left( A \mid B ^ { \prime } \right)$
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2021 Q1 [5]}}