| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tree Diagrams |
| Type | Population partition tree diagram |
| Difficulty | Easy -1.3 This is a straightforward two-stage tree diagram problem with simple percentages and basic probability calculations. It requires only routine application of the multiplication and addition rules for probability, with no conceptual challenges or problem-solving insight needed—typical introductory S1 material that's easier than average A-level questions. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Probability tree diagram drawn correctly | M1 | Tree structure |
| 0.85, 0.15 on first branches | A1 | |
| 0.03, 0.97, 0.06, 0.94 on second branches | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(\text{Not faulty}) = (0.85 \times 0.97) + (0.15 \times 0.94)\) | M1, A1 | Their values, all correct |
| \(= 0.9655\) | A1 | awrt 0.966 |
# Question 1:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Probability tree diagram drawn correctly | M1 | Tree structure |
| 0.85, 0.15 on first branches | A1 | |
| 0.03, 0.97, 0.06, 0.94 on second branches | A1 | |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(\text{Not faulty}) = (0.85 \times 0.97) + (0.15 \times 0.94)$ | M1, A1 | Their values, all correct |
| $= 0.9655$ | A1 | awrt 0.966 |
---\begin{enumerate}
\item A company assembles drills using components from two sources. Goodbuy supplies $85 \%$ of the components and Amart supplies the rest. It is known that $3 \%$ of the components supplied by Goodbuy are faulty and $6 \%$ of those supplied by Amart are faulty.\\
(a) Represent this information on a tree diagram.
\end{enumerate}
An assembled drill is selected at random.\\
(b) Find the probability that it is not faulty.\\
\hfill \mbox{\textit{Edexcel S1 2005 Q1 [6]}}