| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypergeometric Distribution |
| Type | Sequential selection until condition met |
| Difficulty | Standard +0.3 This is a straightforward S1 probability question involving sampling without replacement. While it requires careful counting across multiple parts, each part uses basic probability principles (tree diagrams or direct counting). The conditional probability in part (d) is standard for this level. Slightly easier than average A-level as it's methodical rather than requiring insight. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
\begin{enumerate}
\item Anju has a bag that contains 5 socks of which 2 are blue.
\end{enumerate}
Anju randomly selects socks from the bag, one sock at a time. She does not replace any socks but continues to select socks at random until she has both blue socks.
The discrete random variable $S$ represents the total number of socks that Anju has selected.\\
(a) Write down the value of $\mathrm { P } ( S = 1 )$\\
(b) Find $\mathrm { P } ( S > 2 )$\\
(c) Find $\mathrm { P } ( S = 3 )$\\
(d) Given that the second sock selected is blue, find the probability that Anju selects exactly 3 socks.\\
(e) Find $\mathrm { P } ( S = 5 )$
\hfill \mbox{\textit{Edexcel S1 2018 Q6 [11]}}