| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2004 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Basic Inclusion-Exclusion with Two Sets |
| Difficulty | Easy -1.3 This is a straightforward S1 question requiring direct application of the inclusion-exclusion formula P(A∪B) = P(A) + P(B) - P(A∩B) and basic Venn diagram manipulation. All values are given, requiring only substitution and simple arithmetic with no problem-solving or conceptual insight needed. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| 2 intersecting closed curves in a box | M1 | |
| Both \(\frac{1}{4}\), \(\frac{1}{12}\) placed correctly | B1, B1 | |
| \(\frac{5}{12}\) placed correctly | B1\(\int\) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(P(A \cup B) = \frac{7}{12}\) | B1\(\int\) | 0.583 or \(0.58\dot{3}\) or \(\frac{7}{12}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(P(A | B') = \frac{P(A \cap B')}{P(B')} = \frac{\frac{1}{4}}{\frac{2}{3}} = \frac{3}{8}\) or 0.375 | M1, A1 |
## Question 5:
### Part (a):
| Working | Mark | Guidance |
|---------|------|----------|
| 2 intersecting closed curves in a box | M1 | |
| Both $\frac{1}{4}$, $\frac{1}{12}$ placed correctly | B1, B1 | |
| $\frac{5}{12}$ placed correctly | B1$\int$ | |
### Part (b):
| Working | Mark | Guidance |
|---------|------|----------|
| $P(A \cup B) = \frac{7}{12}$ | B1$\int$ | 0.583 or $0.58\dot{3}$ or $\frac{7}{12}$ |
### Part (c):
| Working | Mark | Guidance |
|---------|------|----------|
| $P(A|B') = \frac{P(A \cap B')}{P(B')} = \frac{\frac{1}{4}}{\frac{2}{3}} = \frac{3}{8}$ or 0.375 | M1, A1 | their fractions divided, cao |
---5. The events $A$ and $B$ are such that $\mathrm { P } ( A ) = \frac { 1 } { 2 } , \mathrm { P } ( B ) = \frac { 1 } { 3 }$ and $\mathrm { P } ( A \cap B ) = \frac { 1 } { 4 }$.
\begin{enumerate}[label=(\alph*)]
\item Using the space below, represent these probabilities in a Venn diagram.
Hence, or otherwise, find
\item $\mathrm { P } ( A \cup B )$,
\item $\mathrm { P } \left( \begin{array} { l l } A & B ^ { \prime } \end{array} \right)$
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2004 Q5 [7]}}