| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Venn diagram with two events |
| Difficulty | Moderate -0.8 This is a straightforward S1 conditional probability question requiring routine application of standard formulas. Part (i) involves basic Venn diagram arithmetic (subtracting intersections), part (ii) checks independence using P(G∩R) = P(G)P(R), and part (iii) applies the conditional probability formula P(R|G) = P(G∩R)/P(G). All values are given directly with no problem-solving or insight required—purely mechanical application of definitions. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| Venn diagram with two labelled intersecting circles \(G\) and \(R\), values: 0.18, 0.06, 0.07, 0.69 | G1 two labelled intersecting circles; G1 at least 2 correct probabilities; G1 remaining probabilities | 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(G) \times P(R) = 0.24 \times 0.13 = 0.0312 \neq P(G \cap R)\) or \(\neq 0.06\), so not independent | M1 for \(0.24 \times 0.13\); A1 | 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(R \mid G) = \frac{P(R \cap G)}{P(G)} = \frac{0.06}{0.24} = \frac{1}{4} = 0.25\) | M1 numerator; M1 denominator; A1 CAO | 3 marks |
## Question 4:
### Part (i)
Venn diagram with two labelled intersecting circles $G$ and $R$, values: 0.18, 0.06, 0.07, 0.69 | G1 two labelled intersecting circles; G1 at least 2 correct probabilities; G1 remaining probabilities | **3 marks**
### Part (ii)
$P(G) \times P(R) = 0.24 \times 0.13 = 0.0312 \neq P(G \cap R)$ or $\neq 0.06$, so not independent | M1 for $0.24 \times 0.13$; A1 | **2 marks**
### Part (iii)
$P(R \mid G) = \frac{P(R \cap G)}{P(G)} = \frac{0.06}{0.24} = \frac{1}{4} = 0.25$ | M1 numerator; M1 denominator; A1 CAO | **3 marks**
---4 In a survey, a large number of young people are asked about their exercise habits. One of these people is selected at random.
\begin{itemize}
\item $G$ is the event that this person goes to the gym.
\item $R$ is the event that this person goes running.
\end{itemize}
You are given that $\mathrm { P } ( G ) = 0.24 , \mathrm { P } ( R ) = 0.13$ and $\mathrm { P } ( G \cap R ) = 0.06$.\\
(i) Draw a Venn diagram, showing the events $G$ and $R$, and fill in the probability corresponding to each of the four regions of your diagram.\\
(ii) Determine whether the events $G$ and $R$ are independent.\\
(iii) Find $\mathrm { P } ( R \mid G )$.
\hfill \mbox{\textit{OCR MEI S1 Q4 [8]}}