WJEC Unit 2 2024 June — Question 3 8 marks

Exam BoardWJEC
ModuleUnit 2 (Unit 2)
Year2024
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndependent Events
TypeVenn diagram with independence constraint
DifficultyModerate -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.
Spec2.03a 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.
  1. Show that \(x = 10\) and find the value of \(y\). [5]
  2. 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]

Question 3:
AnswerMarks
38
Question 3:
3 | 8
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]}}