| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Year | 2024 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Venn diagram with independence constraint |
| Difficulty | Moderate -0.3 Part (a) requires setting up and solving equations using the independence condition P(A∩C) = P(A)×P(C), which is a standard probability technique but involves some algebraic manipulation with the Venn diagram regions. Part (b) is a straightforward conditional probability calculation without replacement. This is typical A-level probability content with no novel insights required, making it slightly easier than average. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
The following Venn diagram shows the participation of 100 students in three activities, $A$, $B$, and $C$, which represent athletics, baseball and climbing respectively.
\includegraphics{figure_3}
For these 100 students, participation in athletics and participation in climbing are independent events.
\begin{enumerate}[label=(\alph*)]
\item Show that $x = 10$ and find the value of $y$. [5]
\item Two students are selected at random, one after the other without replacement. Find the probability that the first student does athletics and the second student does only climbing. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 2024 Q3 [8]}}