| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2024 |
| Session | January |
| Marks | 7 |
| Topic | Conditional Probability |
| Type | At least one success in repeated trials |
| Difficulty | Standard +0.8 This is a multi-part conditional probability question requiring careful counting of combinations from a contingency table. Part (b) requires computing P(A|B) using the definition, and part (c) tests understanding of independence. While the calculations are systematic rather than requiring novel insight, the conditional probability setup and checking independence across multiple overlapping categories makes this moderately challenging, above typical A-level questions but not requiring advanced techniques. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03d Calculate conditional probability: from first principles |
| male | female | |
| black | 1 | 3 |
| yellow | 2 | 1 |
| chocolate | 1 | 1 |
Labrador puppies may be black, yellow or chocolate in colour. Some information about a litter of 9 puppies is given in the table.
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
& male & female \\
\hline
black & 1 & 3 \\
\hline
yellow & 2 & 1 \\
\hline
chocolate & 1 & 1 \\
\hline
\end{tabular}
\end{center}
Four puppies are chosen at random to train as guide dogs.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the probability that at least 3 black puppies are chosen. [3]
\item Determine the probability that exactly 3 females are chosen given that at least 3 black puppies are chosen. [3]
\item Explain whether the 2 events
'choosing exactly 3 females' and 'choosing at least 3 black puppies'
are independent events. [1]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2024 Q5 [7]}}