| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Find unknown probability given independence |
| Difficulty | Moderate -0.8 This is a straightforward application of independence (P(A∩B) = P(A)P(B)) and basic probability rules. Part (a) requires simple division, parts (b-d) use standard formulas with no conceptual challenges. It's routine S1 bookwork testing recall rather than problem-solving, making it easier than average. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(P(B) = 0.12 + 0.4 = 0.3\) | M1 A1 | |
| (b) \(P(A \cup B) = 0.7 - 0.12 = 0.58\) | M1 A1 | |
| (c) \(P(A' \cap B) = 0.3 - 0.12 = 0.18\) | M1 A1 | |
| (d) \(P(A | B') = P(A) = 0.4\) | M1 A1; B1 |
(a) $P(B) = 0.12 + 0.4 = 0.3$ | M1 A1 |
(b) $P(A \cup B) = 0.7 - 0.12 = 0.58$ | M1 A1 |
(c) $P(A' \cap B) = 0.3 - 0.12 = 0.18$ | M1 A1 |
(d) $P(A|B') = P(A) = 0.4$ | M1 A1; B1 | **Total: 7 marks**2. The events $A$ and $B$ are independent. Given that $\mathrm { P } ( A ) = 0.4$ and $\mathrm { P } ( A \cap B ) = 0.12$, find
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { P } ( B )$,
\item $\mathrm { P } ( A \cup B )$,
\item $\mathrm { P } \left( A ^ { \prime } \cap B \right)$,
\item $\mathrm { P } \left( A \mid B ^ { \prime } \right)$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [7]}}