| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Find unknown probability given independence |
| Difficulty | Moderate -0.3 This is a straightforward S1 probability question testing standard set theory identities and the definition of independence. Parts (a)-(b) use De Morgan's laws and the addition rule, while (c)-(d) apply the independence condition P(A∩B)=P(A)P(B) to solve for P(B). All steps follow routine procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.03a Mutually exclusive and independent events2.03d Calculate conditional probability: from first principles |
| Answer | Marks |
|---|---|
| \(1 - 0.6 = 0.4\) | M1 A1 |
| Answer | Marks |
|---|---|
| \(0.6 - 0.2 = 0.4\) | M1 A1 |
| Answer | Marks |
|---|---|
| \(0.6 = 0.2 + P(B) - 0.2P(B)\) | M2 |
| \(0.4 = 0.8P(B); \quad P(B) = 0.5\) | M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(1 - (0.2 \times 0.5) = 0.9\) | M1 A1 | (10) |
**(a)**
$1 - 0.6 = 0.4$ | M1 A1 |
**(b)**
$0.6 - 0.2 = 0.4$ | M1 A1 |
**(c)**
$0.6 = 0.2 + P(B) - 0.2P(B)$ | M2 |
$0.4 = 0.8P(B); \quad P(B) = 0.5$ | M1 A1 |
**(d)**
$1 - (0.2 \times 0.5) = 0.9$ | M1 A1 | (10)
---3. The events $A$ and $B$ are such that
$$\mathrm { P } ( A ) = 0.2 \text { and } \mathrm { P } ( A \cup B ) = 0.6$$
Find
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { P } \left( A ^ { \prime } \cap B ^ { \prime } \right)$,
\item $\quad \mathrm { P } \left( A ^ { \prime } \cap B \right)$.
Given also that events $A$ and $B$ are independent, find
\item $\mathrm { P } ( B )$,
\item $\mathrm { P } \left( A ^ { \prime } \cup B ^ { \prime } \right)$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [10]}}