| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Listing outcomes and counting |
| Difficulty | Moderate -0.8 This is a straightforward counting exercise from S1 requiring students to read a table and apply basic probability definitions (intersection, union, mutual exclusivity, independence). All information is explicitly given; students just need to count carefully and recall standard definitions. Significantly easier than average A-level questions which typically require more problem-solving. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables |
| Competiton | ||||||
| 100 m | 200 m | 110 m hurdles | 400 m | Long jump | ||
| \multirow{10}{*}{Athlete} | Abel | ✓ | ✓ | ✓ | ||
| Bernoulli | ✓ | ✓ | ||||
| Cauchy | ✓ | ✓ | ✓ | |||
| Descartes | ✓ | ✓ | ||||
| Einstein | ✓ | ✓ | ||||
| Fermat | ✓ | ✓ | ||||
| Galois | ✓ | ✓ | ||||
| Hardy | ✓ | ✓ | ✓ | |||
| Iwasawa | ✓ | ✓ | ||||
| Jacobi | ✓ | |||||
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(P(A \cap B) = 0.4\) | B1 CAO | 1 |
| (ii) \(P(C \cup D) = 0.6\) | B1 CAO | 1 |
| (iii) Events B and C are mutually exclusive. | B1 CAO | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.6 \times 0.4 \neq 0.2\) (so B and D not independent) | B1 for \(P(B \cap D) = 0.2\) soi E1 | 2 |
| TOTAL | 5 |
Question 1:
(i) $P(A \cap B) = 0.4$ | B1 CAO | 1
(ii) $P(C \cup D) = 0.6$ | B1 CAO | 1
(iii) Events B and C are mutually exclusive. | B1 CAO | 1
(iv) $P(B) = 0.6$, $P(D) = 0.4$ and $P(B \cap D) = 0.2$
$0.6 \times 0.4 \neq 0.2$ (so B and D not independent) | B1 for $P(B \cap D) = 0.2$ soi E1 | 2
TOTAL | 51 A school athletics team has 10 members. The table shows which competitions each of the members can take part in.
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|}
\hline
& & \multicolumn{5}{|c|}{Competiton} \\
\hline
& & 100 m & 200 m & 110 m hurdles & 400 m & Long jump \\
\hline
\multirow{10}{*}{Athlete} & Abel & ✓ & ✓ & & & ✓ \\
\hline
& Bernoulli & & ✓ & & ✓ & \\
\hline
& Cauchy & ✓ & & ✓ & & ✓ \\
\hline
& Descartes & ✓ & ✓ & & & \\
\hline
& Einstein & & ✓ & & ✓ & \\
\hline
& Fermat & ✓ & & ✓ & & \\
\hline
& Galois & & & & ✓ & ✓ \\
\hline
& Hardy & ✓ & ✓ & & & ✓ \\
\hline
& Iwasawa & & ✓ & & ✓ & \\
\hline
& Jacobi & & & ✓ & & \\
\hline
\end{tabular}
\end{center}
An athlete is selected at random. Events $A , B , C , D$ are defined as follows.\\
$A$ : the athlete can take part in exactly 2 competitions.\\
$B$ : the athlete can take part in the 200 m .\\
$C$ : the athlete can take part in the 110 m hurdles.\\
$D$ : the athlete can take part in the long jump.\\
(i) Write down the value of $\mathrm { P } ( A \cap B )$.\\
(ii) Write down the value of $\mathrm { P } ( C \cup D )$.\\
(iii) Which two of the four events $A , B , C , D$ are mutually exclusive?\\
(iv) Show that events $B$ and $D$ are not independent.
\hfill \mbox{\textit{OCR MEI S1 Q1 [5]}}