| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Probability with replacement/sequential selection |
| Difficulty | Moderate -0.8 This is a straightforward probability question requiring basic counting and application of standard formulas. Parts (a) and (b) involve simple counting and conditional probability with small numbers. Parts (c) and (d) use basic combination formulas (³C₃ and binomial probability) with no conceptual challenges—purely routine S1 material that's easier than average A-level questions. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space5.01a Permutations and combinations: evaluate probabilities |
| Answer | Marks |
|---|---|
| \(\frac{4}{11}\) | A1 |
| Answer | Marks |
|---|---|
| 3 T's, 7 consonants, \(\therefore \frac{3}{7}\) | M1 A1 |
| Answer | Marks |
|---|---|
| \(\frac{3}{11} \times \frac{2}{10} \times \frac{1}{9} = \frac{1}{165}\) | M2 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 vowels: \(\frac{3}{11} \times \frac{2}{10} \times \frac{1}{9} = \frac{1}{165}\) | M1 A1 | |
| 2 vowels: \(3 \times \frac{3}{11} \times \frac{2}{10} \times \frac{7}{9} = \frac{14}{55}\) | M1 A1 | |
| \(P(\text{at least 2 vowels}) = \frac{1}{165} + \frac{14}{55} = \frac{46}{165}\) | M1 A1 | (12) |
**(a)**
$\frac{4}{11}$ | A1 |
**(b)**
3 T's, 7 consonants, $\therefore \frac{3}{7}$ | M1 A1 |
**(c)**
$\frac{3}{11} \times \frac{2}{10} \times \frac{1}{9} = \frac{1}{165}$ | M2 A1 |
**(d)**
3 vowels: $\frac{3}{11} \times \frac{2}{10} \times \frac{1}{9} = \frac{1}{165}$ | M1 A1 |
2 vowels: $3 \times \frac{3}{11} \times \frac{2}{10} \times \frac{7}{9} = \frac{14}{55}$ | M1 A1 |
$P(\text{at least 2 vowels}) = \frac{1}{165} + \frac{14}{55} = \frac{46}{165}$ | M1 A1 | (12)
---6. The individual letters of the word STATISTICAL are written on 11 cards which are then shuffled.
One card is selected at random. Find the probability that it is
\begin{enumerate}[label=(\alph*)]
\item a vowel,
\item a T, given that it is a consonant.
The 11 cards are then shuffled again and the top three are turned over. Find the probability that
\item all three of the cards have a T on them,
\item at least two of the cards show a vowel.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q6 [12]}}