| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2014 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Given conditional, find joint or marginal |
| Difficulty | Moderate -0.8 This is a straightforward S1 conditional probability question requiring direct application of standard formulas: P(A∩B) = P(A|B)×P(B), then using P(A∪B) = P(A) + P(B) - P(A∩B) to find P(A), followed by routine calculations. All parts follow mechanically from the definitions with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature. |
| 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 |
\begin{enumerate}
\item $\quad A$ and $B$ are two events such that
\end{enumerate}
$$\mathrm { P } ( B ) = \frac { 1 } { 2 } \quad \mathrm { P } ( A \mid B ) = \frac { 2 } { 5 } \quad \mathrm { P } ( A \cup B ) = \frac { 13 } { 20 }$$
(a) Find $\mathrm { P } ( A \cap B )$.\\
(b) Draw a Venn diagram to show the events $A , B$ and all the associated probabilities.
Find\\
(c) $\mathrm { P } ( A )$\\
(d) $\mathrm { P } ( B \mid A )$\\
(e) $\mathrm { P } \left( A ^ { \prime } \cap B \right)$\\
\hfill \mbox{\textit{Edexcel S1 2014 Q4 [9]}}