| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2003 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Calculate probabilities using independence |
| Difficulty | Easy -1.2 This question tests basic definitions and straightforward application of independence formulas with simple fractions. Parts (a)-(b) are pure recall, while parts (c)-(e) require only direct substitution into standard formulas (P(A∩B)=P(A)P(B) and addition rule) with no problem-solving or conceptual challenge beyond remembering the definitions. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| Part (a) | ||
| A list of all possible outcomes of an experiment | B1 | (1 mark) |
| Part (b) | ||
| A set of outcomes of an experiment | B1 | (1 mark) |
| Part (c) | ||
| \(P(A \cap B) = P(A)P(B) = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}\) | B1 | (1 mark) |
| Part (d) | ||
| \(P(A | B) = P(A) = \frac{1}{3}\) | M1 |
| \(\frac{1}{3}\) | A1 | (2 marks) |
| Part (e) | ||
| \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\) | M1 | Application of \(P(A \cup B)\) |
| \(= \frac{1}{3} + \frac{1}{4} - \frac{1}{12}\) | ||
| \(= \frac{1}{2}\) | A1 | (2 marks) |
**Part (a)** | |
A list of all possible outcomes of an experiment | B1 | (1 mark)
**Part (b)** | |
A set of outcomes of an experiment | B1 | (1 mark)
**Part (c)** | |
$P(A \cap B) = P(A)P(B) = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}$ | B1 | (1 mark)
**Part (d)** | |
$P(A | B) = P(A) = \frac{1}{3}$ | M1 | Application of indep. |
$\frac{1}{3}$ | A1 | (2 marks)
**Part (e)** | |
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$ | M1 | Application of $P(A \cup B)$ |
$= \frac{1}{3} + \frac{1}{4} - \frac{1}{12}$ | |
$= \frac{1}{2}$ | A1 | (2 marks)
---4. Explain what you understand by
\begin{enumerate}[label=(\alph*)]
\item a sample space,
\item an event.
Two events $A$ and $B$ are independent, such that $\mathrm { P } ( A ) = \frac { 1 } { 3 }$ and $\mathrm { P } ( B ) = \frac { 1 } { 4 }$.\\
Find
\item $\mathrm { P } ( A \cap B )$,
\item $\mathrm { P } ( A B )$,
\item $\mathrm { P } ( A \cup B )$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2003 Q4 [7]}}