| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Venn diagram completion |
| Difficulty | Easy -1.3 This is a straightforward Venn diagram problem requiring basic probability concepts. Part (a) involves translating given percentages into a standard two-set Venn diagram, and part (b) requires simple arithmetic (100% - 31% - 23% - 22% = 24%) to find the intersection. No problem-solving insight needed, just routine application of set notation and percentage calculations. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | 0.22 |
| Answer | Marks |
|---|---|
| 0.31 0.23 | M1 |
| A1 | 1.1 |
| 1.1 | Venn diagram with 2 overlapping regions and 0.22 correctly |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | 0.31 + 0.23 + p(J∩S) = 1 ‒ 0.22 oe |
| 0.24 oe isw | M1 | |
| A1 | 1.1a | |
| 1.1 | may be implied by correct answer or by 24% |
Question 4:
4 | (a) | 0.22
J S
0.31 0.23 | M1
A1 | 1.1
1.1 | Venn diagram with 2 overlapping regions and 0.22 correctly
placed; condone incorrect or no labelling
all probabilities or percentages correctly placed and correctly
labelled; ignore values in intersection
allow if no box drawn
if labels are eg A and B¸ A and B need to be defined
[2]
4 | (b) | 0.31 + 0.23 + p(J∩S) = 1 ‒ 0.22 oe
0.24 oe isw | M1
A1 | 1.1a
1.1 | may be implied by correct answer or by 24%
do not allow 24%
[2]A survey of university students revealed that
\begin{itemize}
\item 31\% have a part-time job but do not play competitive sport.
\item 23\% play competitive sport but do not have a part-time job.
\item 22\% do not play competitive sport and do not have a part-time job.
\end{itemize}
\begin{enumerate}[label=(\alph*)]
\item Show this information on a Venn diagram. [2]
\end{enumerate}
A student is selected at random.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the probability that the student plays competitive sport and has a part-time job. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2022 Q4 [4]}}