| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Three-Set Venn Diagram Probability Calculation |
| Difficulty | Moderate -0.8 This is a straightforward application of reading a completed Venn diagram and calculating basic probabilities. Part (i) requires simple counting and division, while part (ii) involves a standard complement probability calculation with three independent selections. No problem-solving insight or complex reasoning is needed—just careful arithmetic from given information. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
| Answer | Marks | Guidance |
|---|---|---|
| (A) \(P(\text{at most one}) = \frac{83}{100} = 0.83\) | B1 aef | 1 mark |
| (B) \(P(\text{exactly two}) = \frac{10+2+1}{100} = \frac{13}{100} = 0.13\) | M1, A1 aef | M1 for \((10+2+1)/100\); 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(\text{all at least one}) = \frac{53}{100} \times \frac{52}{99} \times \frac{51}{98} = \frac{140556}{970200} = 0.145\) | M1 for \(\frac{53}{100}\times\), M1dep for product of next 2 correct fractions, A1 CAO | Total: 6 marks |
# Question 6:
## Part (i):
(A) $P(\text{at most one}) = \frac{83}{100} = 0.83$ | B1 aef | **1 mark**
(B) $P(\text{exactly two}) = \frac{10+2+1}{100} = \frac{13}{100} = 0.13$ | M1, A1 aef | M1 for $(10+2+1)/100$; **2 marks**
## Part (ii):
$P(\text{all at least one}) = \frac{53}{100} \times \frac{52}{99} \times \frac{51}{98} = \frac{140556}{970200} = 0.145$ | M1 for $\frac{53}{100}\times$, M1dep for product of next 2 correct fractions, A1 CAO | **Total: 6 marks**
---6 Whitefly, blight and mosaic virus are three problems which can affect tomato plants. 100 tomato plants are examined for these problems. The numbers of plants with each type of problem are shown in the Venn diagram. 47 of the plants have none of the problems.\\
\includegraphics[max width=\textwidth, alt={}, center]{3a5d18f5-b1fe-4513-ae4e-f37c20f172b5-3_668_812_998_664}
\begin{enumerate}[label=(\roman*)]
\item One of the 100 plants is selected at random. Find the probability that this plant has\\
(A) at most one of the problems,\\
(B) exactly two of the problems.
\item Three of the 100 plants are selected at random. Find the probability that all of them have at least one of the problems.
Section B (36 marks)
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2009 Q6 [6]}}