| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Incomplete two-way table completion |
| Difficulty | Moderate -0.8 This is a straightforward two-way table completion problem with standard conditional probability calculations. Students need to organize given information, complete a table by subtraction, and apply basic probability formulas including P(A|B) and the law of total probability. All steps are routine S1 techniques with no conceptual challenges or novel insights required. |
| Spec | 2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| Glasses | No Glasses | Totals |
| Science | 18 | 12 |
| Arts | 27 | 23 |
| Humanities | 44 | 24 |
| Totals | 89 | 59 |
| 50 may be seen in (a); 23 may be seen in (b) | B1, B1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(\text{Arts}) = \frac{50}{148} = \frac{25}{74} = 0.338\) | M1 A1 | a number/148 |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(\text{No glasses} \mid \text{Arts}) = \frac{23/148}{50/148} = \frac{23}{50} = 0.46\) | M1 A1 | \(\frac{\text{prob}}{\text{their (a) prob}}\) or \(\frac{\text{number}}{\text{their } 50}\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(\text{Right Handed}) = \left(\frac{30}{148} \times 0.8\right) + \left(\frac{50}{148} \times 0.7\right) + \left(\frac{68}{148} \times 0.75\right)\) | M1 A1\(\sqrt{}\) | Attempt add three prob; A1\(\sqrt{}\) on their (a) |
| \(= \frac{55}{74} = 0.743\) | A1 | awrt 0.743 |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(\text{Science} \mid \text{Right handed}) = \frac{\frac{30}{148} \times 0.8}{(c)} = \frac{12}{55} = 0.218\) | M1 A1\(\sqrt{}\) A1 | \(\sqrt{}\) on their (c) |
# Question 7:
**Completed table:**
| | Glasses | No Glasses | Totals |
|---|---|---|---|
| Science | 18 | **12** | 30 |
| Arts | **27** | **23** | 50 |
| Humanities | 44 | **24** | 68 |
| Totals | 89 | **59** | 148 |
50 may be seen in (a); 23 may be seen in (b) | B1, B1 |
## Part (a)
$P(\text{Arts}) = \frac{50}{148} = \frac{25}{74} = 0.338$ | M1 A1 | a number/148
## Part (b)
$P(\text{No glasses} \mid \text{Arts}) = \frac{23/148}{50/148} = \frac{23}{50} = 0.46$ | M1 A1 | $\frac{\text{prob}}{\text{their (a) prob}}$ or $\frac{\text{number}}{\text{their } 50}$
## Part (c)
$P(\text{Right Handed}) = \left(\frac{30}{148} \times 0.8\right) + \left(\frac{50}{148} \times 0.7\right) + \left(\frac{68}{148} \times 0.75\right)$ | M1 A1$\sqrt{}$ | Attempt add three prob; A1$\sqrt{}$ on their (a)
$= \frac{55}{74} = 0.743$ | A1 | awrt 0.743
## Part (d)
$P(\text{Science} \mid \text{Right handed}) = \frac{\frac{30}{148} \times 0.8}{(c)} = \frac{12}{55} = 0.218$ | M1 A1$\sqrt{}$ A1 | $\sqrt{}$ on their (c)
The image appears to be essentially blank — it only shows the header "PhysicsAndMathsTutor.com" and the footer identifying it as "6683 Statistics S1, June 2005 Advanced Subsidiary/Advanced Level in GCE Mathematics." There is no mark scheme content visible on this page to extract.
Could you please share the actual pages containing the mark scheme questions and answers? This appears to be a blank/cover page only.7. In a school there are 148 students in Years 12 and 13 studying Science, Humanities or Arts subjects. Of these students, 89 wear glasses and the others do not. There are 30 Science students of whom 18 wear glasses. The corresponding figures for the Humanities students are 68 and 44 respectively.
A student is chosen at random.
Find the probability that this student
\begin{enumerate}[label=(\alph*)]
\item is studying Arts subjects,
\item does not wear glasses, given that the student is studying Arts subjects.
Amongst the Science students, $80 \%$ are right-handed. Corresponding percentages for Humanities and Arts students are 75\% and 70\% respectively.
A student is again chosen at random.
\item Find the probability that this student is right-handed.
\item Given that this student is right-handed, find the probability that the student is studying Science subjects.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2005 Q7 [12]}}