| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Complement and union/intersection laws |
| Difficulty | Moderate -0.3 This is a straightforward S1 probability question testing basic set notation and conditional probability. Students are given most probabilities directly and need to apply standard formulas (P(A∪B) = 1 - P(A'∩B'), conditional probability definition, and independence test). The complement information makes part (a) particularly routine, and all parts follow standard textbook patterns with no novel problem-solving required. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| \(1 - 0.22 = 0.78\) | M1 A1 | |
| \(0.78 - 0.35 = 0.43\) | M1 A1 | |
| \(\frac{P(A \cap B)}{P(A)} = \frac{0.7 - 0.43}{0.7} = 0.386\) (3sf) | M2 A1 | |
| not independent as e.g. \(P(B \mid A) \neq P(B)\) | B2 | (9) |
$1 - 0.22 = 0.78$ | M1 A1 |
$0.78 - 0.35 = 0.43$ | M1 A1 |
$\frac{P(A \cap B)}{P(A)} = \frac{0.7 - 0.43}{0.7} = 0.386$ (3sf) | M2 A1 |
not independent as e.g. $P(B \mid A) \neq P(B)$ | B2 | (9)3. The probability that Ajita gets up before 6.30 am in the morning is 0.7
The probability that she goes for a run in the morning is 0.35\\
The probability that Ajita gets up after 6.30 am and does not go for a run is 0.22\\
Let $A$ represent the event that Ajita gets up before 6.30 am and $B$ represent the event that she goes for a run in the morning.
Find
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { P } ( A \cup B )$,
\item $\mathrm { P } \left( A \cap B ^ { \prime } \right)$,
\item $\mathrm { P } ( B \mid A )$.
\item State, with a reason, whether or not events $A$ and $B$ are independent.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [9]}}