| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2024 |
| Session | September |
| Marks | 4 |
| Topic | Conditional Probability |
| Type | Finding unknown probability from total probability |
| Difficulty | Moderate -0.8 This is a straightforward conditional probability problem using the law of total probability. Part (a) requires basic algebraic manipulation with percentages (setting up 0.1×0.09 + 0.3×0.03 + 0.6×p = 0.06 and solving for p). Part (b) tests understanding of independence by comparing P(B) with P(B|faulty), which is routine bookwork. The question involves only standard techniques with no problem-solving insight required, making it easier than average but not trivial since it requires careful setup. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
A factory buys 10\% of its components from supplier $A$, 30\% from supplier $B$ and the rest from supplier $C$. It is known that 6\% of the components it buys are faulty.
Of the components bought from supplier $A$, 9\% are faulty and of the components bought from supplier $B$, 3\% are faulty.
\begin{enumerate}[label=(\alph*)]
\item Find the percentage of components bought from supplier $C$ that are faulty. [3]
\end{enumerate}
A component is selected at random.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Explain why the event "the component was bought from supplier $B$" is not statistically independent from the event "the component is faulty". [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2024 Q2 [4]}}