| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Venn diagram completion |
| Difficulty | Easy -1.2 This is a straightforward Venn diagram reading exercise requiring only basic probability calculations (counting regions and dividing by totals). All parts involve simple arithmetic with no conceptual challenges—students just need to identify the correct regions and apply P(A) = n(A)/n(total). The conditional probability in (ii) and the 'exactly one' calculation in (iii) add minimal complexity but remain routine applications of standard formulas. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| (A) \(P(\text{at least one}) = \frac{36}{50} = \frac{18}{25} = 0.72\) | B1 | aef |
| (B) \(P(\text{exactly one}) = \frac{9+6+5}{50} = \frac{20}{50} = \frac{2}{5} = 0.4\) | M1 | for \((9+6+5)/50\) |
| A1 | aef |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(\text{not paper} \mid \text{aluminium}) = \frac{13}{24}\) | M1 | for denominator \(24\) or \(24/50\) or \(0.48\) |
| A1 | CAO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(\text{one kitchen waste}) = 2 \times \frac{18}{50} \times \frac{32}{49} = \frac{576}{1225} = 0.470\) | M1 | for both fractions |
| M1 | for \(2 \times\) product of both, or sum of 2 pairs | |
| A1 |
## Question 4:
### Part (i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| (A) $P(\text{at least one}) = \frac{36}{50} = \frac{18}{25} = 0.72$ | B1 | aef |
| (B) $P(\text{exactly one}) = \frac{9+6+5}{50} = \frac{20}{50} = \frac{2}{5} = 0.4$ | M1 | for $(9+6+5)/50$ |
| | A1 | aef |
### Part (ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(\text{not paper} \mid \text{aluminium}) = \frac{13}{24}$ | M1 | for denominator $24$ or $24/50$ or $0.48$ |
| | A1 | CAO |
### Part (iii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(\text{one kitchen waste}) = 2 \times \frac{18}{50} \times \frac{32}{49} = \frac{576}{1225} = 0.470$ | M1 | for both fractions |
| | M1 | for $2 \times$ product of both, or sum of 2 pairs |
| | A1 | |4 A local council has introduced a recycling scheme for aluminium, paper and kitchen waste. 50 residents are asked which of these materials they recycle. The numbers of people who recycle each type of material are shown in the Venn diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{b56ccabe-0e51-4555-b550-78ba347f69bb-3_803_804_520_717}
One of the residents is selected at random.
\begin{enumerate}[label=(\roman*)]
\item Find the probability that this resident recycles\\
(A) at least one of the materials,\\
(B) exactly one of the materials.
\item Given that the resident recycles aluminium, find the probability that this resident does not recycle paper.
Two residents are selected at random.
\item Find the probability that exactly one of them recycles kitchen waste.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q4 [8]}}