| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Calculate probabilities using independence |
| Difficulty | Standard +0.3 This is a straightforward application of independence and probability rules. Students must recognize that P(A∩B') = P(A) - P(A∩B), then use independence P(A∩B) = P(A)P(B) to find P(B), and finally apply complement rules. While it requires multiple steps, each step follows standard S1 techniques with no novel insight needed, making it slightly easier than average. |
| Spec | 2.03a Mutually exclusive and independent events2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\frac{3}{4} - \frac{1}{4} = \frac{1}{2}\) | M1 A1 | |
| (b) \(\frac{1}{3} \times P(B) = \frac{1}{2} \therefore P(B) = \frac{2}{3}\) | M2 A1 | |
| (c) \(1 - [P(B) + P(A \cap B')] = 1 - (\frac{2}{3} + \frac{1}{3}) = \frac{1}{12}\) | M2 A1 | (8 marks) |
(a) $\frac{3}{4} - \frac{1}{4} = \frac{1}{2}$ | M1 A1 |
(b) $\frac{1}{3} \times P(B) = \frac{1}{2} \therefore P(B) = \frac{2}{3}$ | M2 A1 |
(c) $1 - [P(B) + P(A \cap B')] = 1 - (\frac{2}{3} + \frac{1}{3}) = \frac{1}{12}$ | M2 A1 | (8 marks)
---2. Events $A$ and $B$ are independent.
Given also that
$$\mathrm { P } ( A ) = \frac { 3 } { 4 } \quad \text { and } \quad \mathrm { P } \left( A \cap B ^ { \prime } \right) = \frac { 1 } { 4 }$$
Find
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { P } ( A \cap B )$,
\item $\mathrm { P } ( B )$,
\item $\mathrm { P } \left( A ^ { \prime } \cap B ^ { \prime } \right)$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q2 [8]}}