| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Listing outcomes and counting |
| Difficulty | Easy -1.8 This is a very routine question requiring only basic LCM calculation (filling in 5 missing table entries), counting outcomes from a completed table, and applying the definition of independence P(A∩B)=P(A)P(B). No problem-solving or insight needed—purely mechanical arithmetic and recall of a standard formula. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Second integer | |||||||||
| \cline { 2 - 8 } \multicolumn{2}{|c|}{} | 1 | 2 | 3 | 4 | 5 | 6 | |||
\multirow{5}{*}{
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | ||
| \cline { 2 - 8 } | 2 | 2 | 2 | 6 | 4 | 10 | 6 | ||
| \cline { 2 - 8 } | 3 | 3 | 6 | 3 | 12 | 15 | 6 | ||
| \cline { 2 - 8 } | 4 | 4 | 4 | 12 | 12 | ||||
| \cline { 2 - 8 } | 5 | 5 | 10 | 15 | |||||
| \cline { 2 - 8 } | 6 | 6 | 6 | 6 | 12 | ||||
| Answer | Marks | Guidance |
|---|---|---|
| LCM table (6×6 grid) with all values correct | B1 | All correct |
| Answer | Marks |
|---|---|
| (A) \(P(\text{LCM} > 6) = \frac{1}{?}\) | B1 |
| (B) \(P(\text{LCM} = 5n) = \frac{11}{36}\) | B1 |
| (C) \(P(\text{LCM} > 6 \cap \text{LCM} = 5n) = \frac{2}{9}\) | M1 use of diagram; A1 cao |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{3} \times \frac{11}{36} \neq \frac{2}{9}\), hence events are not independent | M1 use of definition | E1 |
## Question 3:
### Part (i):
LCM table (6×6 grid) with all values correct | B1 | All correct
### Part (ii):
**(A)** $P(\text{LCM} > 6) = \frac{1}{?}$ | B1 |
**(B)** $P(\text{LCM} = 5n) = \frac{11}{36}$ | B1 |
**(C)** $P(\text{LCM} > 6 \cap \text{LCM} = 5n) = \frac{2}{9}$ | M1 use of diagram; A1 cao |
### Part (iii):
$\frac{1}{3} \times \frac{11}{36} \neq \frac{2}{9}$, hence events are not independent | M1 use of definition | E1
---\begin{enumerate}[label=(\roman*)]
\item On die insert, complete the lable giving due lowest common multiples of all pairs of integers between 1 and 6 .
\begin{center}
\begin{tabular}{ | l | r | | r | r | r | r | r | r | }
\hline
\multicolumn{2}{|c|}{} & \multicolumn{6}{|c|}{Second integer} \\
\cline { 2 - 8 }
\multicolumn{2}{|c|}{} & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline\hline
\multirow{5}{*}{\begin{tabular}{ l }
First \\
integer \\
\end{tabular}} & 1 & 1 & 2 & 3 & 4 & 5 & 6 \\
\cline { 2 - 8 }
& 2 & 2 & 2 & 6 & 4 & 10 & 6 \\
\cline { 2 - 8 }
& 3 & 3 & 6 & 3 & 12 & 15 & 6 \\
\cline { 2 - 8 }
& 4 & 4 & 4 & 12 & & & 12 \\
\cline { 2 - 8 }
& 5 & 5 & 10 & 15 & & & \\
\cline { 2 - 8 }
& 6 & 6 & 6 & 6 & 12 & & \\
\hline
\end{tabular}
\end{center}
Two fair dice are thrown and the lowest common multiple of the two scores is found.
\item Use the table to find the probabilities of the following events.\\
(A) The lowest common multiple is greater than 6 .\\
(B) The lowest common multiple is a multiple of 5 .\\
(C) The lowest common multiple is both greater than 6 and a multiple of 5.
\item Use your answers to part (ii) to show that the events "the lowest common multiple is greater than 6 " and "the lowest common multiple is a multiple of 5 " are not independent.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q3 [6]}}