| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Both independence and mutual exclusivity |
| Difficulty | Moderate -0.3 This is a straightforward probability question testing standard formulas and definitions. Part (a) uses the addition rule P(A∪B) = P(A) + P(B) - P(A∩B), parts (b)(i-ii) check definitions of mutual exclusivity and independence using given values, part (c) applies conditional probability P(B|A) = P(A∩B)/P(A), and part (d) requires finding P(A'∩B') then dividing by P(B'). All techniques are routine S1 content with no problem-solving insight required, though part (d) adds a minor computational step. Slightly easier than average due to being purely procedural. |
| 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) \(0.88 = P(A) + 0.52 - 0.24\), so \(P(A) = 0.6\) | M1 A1 A1 | |
| (b) (i) No: \(P(A \cap B) \neq 0\) | M1 A1 | |
| (ii) No: \(0.6 \times 0.52 \neq 0.24\) | M1 A1 | |
| (c) \(P(B | A) = 0.24 \div 0.6 = 0.4\) | M1 A1 |
| (d) \(P(A' | B') = P(A' \cap B')/P(B') = 0.12 \div 0.48 = 0.25\) | M1 A1 A1 |
| 12 marks total |
(a) $0.88 = P(A) + 0.52 - 0.24$, so $P(A) = 0.6$ | M1 A1 A1 |
(b) (i) No: $P(A \cap B) \neq 0$ | M1 A1 |
(ii) No: $0.6 \times 0.52 \neq 0.24$ | M1 A1 |
(c) $P(B|A) = 0.24 \div 0.6 = 0.4$ | M1 A1 |
(d) $P(A'|B') = P(A' \cap B')/P(B') = 0.12 \div 0.48 = 0.25$ | M1 A1 A1 |
| 12 marks total |The events $A$ and $B$ are such that P$(A \cap B) = 0.24$, P$(A \cup B) = 0.88$ and P$(B) = 0.52$.
\begin{enumerate}[label=(\alph*)]
\item Find P$(A)$. [3 marks]
\item Determine, with reasons, whether $A$ and $B$ are \begin{enumerate}[label=(\roman*)] \item mutually exclusive, \item independent. \end{enumerate} [4 marks]
\item Find P$(B | A)$. [2 marks]
\item Find P$(A' | B')$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q5 [12]}}