| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Both independence and mutual exclusivity |
| Difficulty | Moderate -0.8 This is a straightforward probability question testing basic definitions. Part (a) requires only checking if P(A ∩ B) = 0, which is immediate. Part (b) requires finding P(B) using the addition rule (one step), then checking if P(A ∩ B) = P(A)P(B) (one multiplication). Both parts are direct application of definitions with minimal calculation, making this easier than average. |
| Spec | 2.03a Mutually exclusive and independent events |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(P(A \cap B) \neq 0\), so not mutually exclusive | B1 | |
| (b) \(0.65 = 0.3 + P(B) - 0.15\) so \(P(B) = 0.5\) | M1 A1 | |
| \(P(A) \times P(B) = 0.3 \times 0.5 = 0.15 = P(A \cap B)\), so independent | A1 | Total: 4 marks |
(a) $P(A \cap B) \neq 0$, so not mutually exclusive | B1 |
(b) $0.65 = 0.3 + P(B) - 0.15$ so $P(B) = 0.5$ | M1 A1 |
$P(A) \times P(B) = 0.3 \times 0.5 = 0.15 = P(A \cap B)$, so independent | A1 | **Total: 4 marks**Given that $P(A \cup B) = 0.65$, $P(A \cap B) = 0.15$ and $P(A) = 0.3$, determine, with explanation, whether or not the events $A$ and $B$ are
\begin{enumerate}[label=(\alph*)]
\item mutually exclusive, [1 mark]
\item independent. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q1 [4]}}