SPS SPS FM Statistics 2021 June — Question 2 8 marks

Exam BoardSPS
ModuleSPS FM Statistics (SPS FM Statistics)
Year2021
SessionJune
Marks8
TopicConditional Probability
TypeGiven conditional, find joint or marginal
DifficultyModerate -0.3 This is a straightforward probability question testing standard formulas (conditional probability, union/intersection rules) with clear algebraic steps. While it requires careful manipulation across three parts, the techniques are routine for Further Maths students and no conceptual insight is needed—slightly easier than average.
Spec2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles

Events \(A\) and \(B\) are such that \(P(A \cup B) = 0.95\), \(P(A \cap B) = 0.6\) and \(P(A|B) = 0.75\).
  1. Find \(P(B)\). [3]
  2. Find \(P(A)\). [3]
  3. Show that the events \(A'\) and \(B\) are independent. [2]

Events $A$ and $B$ are such that $P(A \cup B) = 0.95$, $P(A \cap B) = 0.6$ and $P(A|B) = 0.75$.

\begin{enumerate}[label=(\roman*)]
\item Find $P(B)$. [3]
\item Find $P(A)$. [3]
\item Show that the events $A'$ and $B$ are independent. [2]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q2 [8]}}