| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2021 |
| Session | May |
| Marks | 8 |
| Topic | Conditional Probability |
| Type | Conditional probability with algebraic expressions |
| Difficulty | Standard +0.3 This is a straightforward conditional probability question requiring application of standard formulas P(C|D) = P(C∩D)/P(D) and manipulation of probability laws. Part (a) is immediate from definitions, and part (b) involves algebraic manipulation of given relationships using complement rules—routine for A-level statistics with no novel insight required, making it slightly easier than average. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
5. Two events C and D are such that $P ( C \mid D ) = 3 \times P ( C )$ where $P ( C ) \neq 0$.
\begin{enumerate}[label=(\alph*)]
\item Explain whether or not events C and D could be independent events.
Given also that
$$P ( C \cap D ) = \frac { 1 } { 2 } \times P ( C ) \text { and } P \left( C ^ { \prime } \cap D ^ { \prime } \right) = \frac { 7 } { 10 }$$
\item find $P ( C )$, showing your working clearly.
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2021 Q5 [8]}}