| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2025 |
| Session | January |
| Marks | 8 |
| Topic | Independent Events |
| Type | Venn diagram with independence constraint |
| Difficulty | Moderate -0.8 This is a straightforward application of conditional probability and independence definitions. Part (i) uses the basic formula P(A∩B) = P(B|A)×P(A). Parts (ii-iv) involve routine Venn diagram completion and checking independence using standard definitions. All steps are mechanical with no problem-solving insight required, making this easier than average. |
| Spec | 2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
\begin{enumerate}
\item Isobel plays football for a local team. Sometimes her parents attend matches to watch her play.
\end{enumerate}
\begin{itemize}
\item $A$ is the event that Isobel's parents watch a match.
\item $B$ is the event that Isobel scores in a match.
\end{itemize}
You are given that $\mathrm { P } ( B \mid A ) = \frac { 3 } { 7 }$ and $\mathrm { P } ( A ) = \frac { 7 } { 10 }$.\\
(i) Calculate $\mathrm { P } ( A \cap B )$.
The probability that Isobel does not score and her parents do not attend is 0.1 .\\
(ii) Draw a Venn diagram showing the events $A$ and $B$, and mark in the probability corresponding to each of the regions of your diagram.\\
(iii) Are events $A$ and $B$ independent? Give a reason for your answer.\\
(iv) By comparing $\mathrm { P } ( B \backslash A )$ with $\mathrm { P } ( B )$, explain why Isobel should ask her parents not to attend.\\[0pt]
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\hfill \mbox{\textit{SPS SPS SM Statistics 2025 Q1 [8]}}