| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2002 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Independent events test |
| Difficulty | Easy -1.2 This is a straightforward recall question testing basic probability definitions. Students only need to check if P(A and B) = P(A)×P(B) for independence (0.4 ≠ 0.24) and if P(A and B) = 0 for mutual exclusivity (0.4 ≠ 0). No problem-solving or multi-step reasoning required, just direct application of memorized definitions. |
| Spec | 2.03a Mutually exclusive and independent events |
| Answer | Marks |
|---|---|
| \(P(A) \times P(B) \neq P(A \text{ and } B)\) | B1, B1dep2 |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(A \text{ and } B) \neq 0\) | B1, B1 2 | Can be stated in words |
**(i) not independent**
$P(A) \times P(B) \neq P(A \text{ and } B)$ | B1, B1dep2 |
**(ii) not mutually exclusive**
$P(A \text{ and } B) \neq 0$ | B1, B1 2 | Can be stated in wordsEvents $A$ and $B$ are such that $\text{P}(A) = 0.3$, $\text{P}(B) = 0.8$ and $\text{P}(A \text{ and } B) = 0.4$. State, giving a reason in each case, whether events $A$ and $B$ are
\begin{enumerate}[label=(\roman*)]
\item independent, [2]
\item mutually exclusive. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2002 Q1 [4]}}