| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Three-Set Venn Diagram Construction |
| Difficulty | Moderate -0.3 This is a standard Venn diagram question with three sets requiring straightforward application of inclusion-exclusion to fill in regions, followed by basic probability calculations. While it has multiple parts (9 marks total), each step is routine: subtract overlaps to find individual regions, then compute simple probabilities. The conditional probability in part (d) requires identifying the correct subset but involves no complex reasoning. Slightly easier than average due to being a textbook application with no novel problem-solving required. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks |
|---|---|
| Marks: M1 M1 A1 A1 B1 | (5) |
| Answer | Marks |
|---|---|
| Marks: B1ft | (1) |
| Answer | Marks |
|---|---|
| Marks: B1ft | (1) |
| Answer | Marks |
|---|---|
| Marks: M1 A1 | (2) |
## Part (a)
**Answer:** 3 closed curves and 4 in centre. Evidence of subtraction. 31, 36, 24, 41, 17, 11. Labels on loops, 16 and box
**Marks:** M1 M1 A1 A1 B1 | (5)
## Part (b)
**Answer:** $P(\text{None of the 3 options}) = \frac{16}{180} = \frac{4}{45}$
**Marks:** B1ft | (1)
**Guidance:**
- B1ft for $\frac{16}{180}$ or any exact equivalent. Can fit their "16" from their box. If there is no value for their "16" in the box only allow this mark if they have shown some working
## Part (c)
**Answer:** $P(\text{Networking only}) = \frac{17}{180}$
**Marks:** B1ft | (1)
**Guidance:**
- B1ft fit their "17". Accept any exact equivalent
## Part (d)
**Answer:** $P(\text{All 3 options/technician}) = \frac{4}{40} = \frac{1}{10}$
**Marks:** M1 A1 | (2)
**Guidance:**
---There are 180 students at a college following a general course in computing. Students on this course can choose to take up to three extra options.
112 take systems support,
70 take developing software,
81 take networking,
35 take developing software and systems support,
28 take networking and developing software,
40 take systems support and networking,
4 take all three extra options.
\begin{enumerate}[label=(\alph*)]
\item In the space below, draw a Venn diagram to represent this information. [5]
\end{enumerate}
A student from the course is chosen at random.
Find the probability that this student takes
\begin{enumerate}[label=(\alph*), start=2]
\item none of the three extra options, [1]
\item networking only. [1]
\end{enumerate}
Students who want to become technicians take systems support and networking. Given that a randomly chosen student wants to become a technician,
\begin{enumerate}[label=(\alph*), start=4]
\item find the probability that this student takes all three extra options. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2010 Q4 [9]}}