| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Test independence using definition |
| Difficulty | Moderate -0.3 This is a standard S1 probability question requiring systematic application of probability rules (addition rule, conditional probability, mutual exclusivity) and simultaneous equations. While it has multiple parts and requires careful algebraic manipulation, the techniques are routine for A-level and no novel insight is needed—slightly easier than average due to its procedural nature. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(0·6 = x + y - 0·2x\) → \(0·8x + y = 0·6\) → \(4x + 5y = 3\) | M1 A1 | |
| (b) \(0·9 = y + (x + y)\) → \(x + 2y = 0·9\) | M1 A1 | |
| Solve: \(y = 0·2\), \(x = 0·5\) | M1 A1 | |
| (c) \(P(B | A) = P(B)\), so \(A\) and \(B\) are independent | M1 A1 |
(a) $0·6 = x + y - 0·2x$ → $0·8x + y = 0·6$ → $4x + 5y = 3$ | M1 A1 |
(b) $0·9 = y + (x + y)$ → $x + 2y = 0·9$ | M1 A1 |
Solve: $y = 0·2$, $x = 0·5$ | M1 A1 |
(c) $P(B|A) = P(B)$, so $A$ and $B$ are independent | M1 A1 | 8 marks total$A$, $B$ and $C$ are three events such that $\text{P}(A) = x$, $\text{P}(B) = y$ and $\text{P}(C) = x + y$.
It is known that $\text{P}(A \cup B) = 0.6$ and $\text{P}(B \mid A) = 0.2$.
\begin{enumerate}[label=(\alph*)]
\item Show that $4x + 5y = 3$. [2 marks]
\end{enumerate}
It is also known that $B$ and $C$ are mutually exclusive and that $\text{P}(B \cup C) = 0.9$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Obtain another equation in $x$ and $y$ and hence find the values of $x$ and $y$. [4 marks]
\item Deduce whether or not $A$ and $B$ are independent events. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [8]}}