| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tree Diagrams |
| Type | Calculate combined outcome probability |
| Difficulty | Easy -1.3 This is a straightforward S1 tree diagram question with simple counting (4 beads total, small numbers) and basic probability without replacement. Part (a) is routine construction, part (b) requires identifying two favorable outcomes from the tree and adding their probabilities—standard textbook exercise with no conceptual challenges. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks |
|---|---|
| Marks: M1 A1 A1 | (3) |
| Answer | Marks |
|---|---|
| Marks: M1 A1 | (2) |
## Part (a)
**Answer:** Probability tree with 3 branches followed by 3, 2, 2 with labels R, B, G seen. Allow 3 branches followed by 3, 3, 3 if 0 probabilities are seen implying that 3, 2, 2 intended. Allow blank branches if the other probabilities imply probability on blanks is zero. Ignore further sets of branches.
**Marks:** M1 A1 A1 | (3)
**Guidance:**
- 1st A1 for correct probabilities and correct labels on 1st set of branches
- 2nd A1 for correct probabilities and correct labels on 2nd set of branches
- Accept 0.33, 0.67 etc or better here
## Part (b)
**Answer:** $P(\text{Blue bead and a green bead}) = \left(\frac{1}{4} \times \frac{1}{3}\right) + \left(\frac{1}{4} \times \frac{1}{3}\right) = \frac{1}{6}$ (or any exact equivalent)
**Marks:** M1 A1 | (2)
**Guidance:**
- M1 for identifying the 2 cases BG and GB and adding 2 products of probabilities. These cases may be identified by their probabilities e.g. $\left(\frac{1}{4} \times \frac{1}{3}\right) + \left(\frac{1}{4} \times \frac{1}{3}\right)$
- NB $\frac{1}{6}$ (or exact equivalent) with no working scores 2/2
---A jar contains 2 red, 1 blue and 1 green bead. Two beads are drawn at random from the jar without replacement.
\begin{enumerate}[label=(\alph*)]
\item In the space below, draw a tree diagram to illustrate all the possible outcomes and associated probabilities. State your probabilities clearly. [3]
\item Find the probability that a blue bead and a green bead are drawn from the jar. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2010 Q1 [5]}}