| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Venn diagram with three events |
| Difficulty | Moderate -0.8 This is a straightforward Venn diagram reading exercise requiring basic probability calculations (reading values, simple addition/subtraction) and one conditional probability application using P(A|B) = P(A∩B)/P(B). All values are given directly in the diagram with no algebraic setup needed, making it easier than average. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
# Question 1
## (i) (A)
$P(\text{Watched cyc but not fb}) = \frac{15}{250} = \frac{3}{50} = 0.06$
B1 CAO (aef)
[1]
## (i) (B)
$P(\text{Watched one or two}) = \frac{33+12+21+14+3+65}{250}$
$= \frac{148}{250} = \frac{74}{125} = 0.592$
M1 For M1 terms must be added with no extra terms (added or subtracted)
A1 CAO (aef)
[2]
OR: $\frac{250-(64+38)}{250}$
## (ii)
$P(\text{Not watched fb} \mid \text{watched cyc}) = \frac{15}{67} = 0.224$ (0.223880597...)
M1 For denominator of either 67 or 67/250 or 0.268
A1 CAO (aef)
[2]
Allow 0.22 with working1 A survey is being carried out into the sports viewing habits of people in a particular area. As part of the survey, 250 people are asked which of the following sports they have watched on television in the past month.
\begin{itemize}
\item Football
\item Cycling
\item Rugby
\end{itemize}
The numbers of people who have watched these sports are shown in the Venn diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{870b6ef1-60f7-42e3-95f8-0544a2a07b15-1_725_921_728_622}
One of the people is selected at random.
\begin{enumerate}[label=(\roman*)]
\item Find the probability that this person has in the past month\\
(A) watched cycling but not football,\\
(B) watched either one or two of the three sports.
\item Given that this person has watched cycling, find the probability that this person has not watched football.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q1 [5]}}