| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Basic probability calculation |
| Difficulty | Easy -1.3 This is a straightforward probability question requiring basic counting and understanding of even/odd numbers and primes. Parts (a)-(c) are simple identification from a small sample space, while part (d) requires recognizing that sum is even when both rolls have same parity, but still involves only basic probability multiplication—well below average A-level difficulty. |
| Spec | 2.03a Mutually exclusive and independent events |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(p(A) = \frac{1}{3}\) o.e. | B1 | e.g. \(\frac{2}{6}\) etc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(p(B) = \frac{1}{2}\) o.e. | B1 | e.g. \(\frac{3}{6}\) etc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{5}{6}\) | B1FT | FT their \(\frac{1}{3} + \frac{1}{2}\) provided their probability total \(\leq 1\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(p(\text{odd, odd}) + p(\text{even, even})\) soi or \(1 - p(\text{odd, even})\) etc | M1 | Can score this mark for the intention to calculate \(p(\text{odd, odd}) + p(\text{even, even})\) - may be stated, or partial cases listed, or with a tree diagram with correct pathways or with a statement of 'odd, odd' and 'even, even' and an attempt to add. |
| \(\left(\frac{2}{3}\right)^2 + \left(\frac{1}{3}\right)^2\) | A1 | |
| \(\frac{5}{9}\) o.e. \(\frac{20}{36}\) etc | A1 | allow \(0.\dot{5}\) correct to 3 dp or better so \(0.555\ldots\) or \(0.555\) but not \(0.55\) however isw once \(\frac{5}{9}\) o.e. seen. Condone \(0.556\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Complete sample space diagram (as shown with sums of two dice ranging from 2 to 14) | M1 | 3.1a - Complete sample space diagram with maximum two errors |
| Extraction of even outcomes (underlined values in diagram) | A1 | 2.1 - Extraction of even outcomes - may circle or underline etc. |
| \(\frac{5}{9}\) o.e. \(\frac{20}{36}\) etc | A1 | 1.1 - Allow \(0.\dot{5}\) correct to 3 dp or better so 0.555… or 0.555 but not 0.55 however isw once \(\frac{5}{9}\) o.e. seen. Condone 0.556 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Listing cases: \((1,3)\ (1,5)\ (1,7)\ (3,5)\ (3,7)\ (4,6)\ (5,7)\) x2 and \((1,1)\ (3,3)\ (4,4)\ (5,5)\ (6,6)\ (7,7)\) | M1 | 3.1a - Must make a clear attempt at pairing odd with odd and even with even. List can be incomplete for this mark |
| A complete list extracted | A1 | 2.1 - May be implied by a correct answer |
| \(\frac{5}{9}\) o.e. \(\frac{20}{36}\) etc | A1 | 1.1 - Allow \(0.\dot{5}\) correct to 3 dp or better so 0.555… but not 0.55 however isw once \(\frac{5}{9}\) o.e. seen. Condone 0.556 |
## Question 9:
### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $p(A) = \frac{1}{3}$ o.e. | B1 | e.g. $\frac{2}{6}$ etc |
### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $p(B) = \frac{1}{2}$ o.e. | B1 | e.g. $\frac{3}{6}$ etc |
### Part (c):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{5}{6}$ | B1FT | FT their $\frac{1}{3} + \frac{1}{2}$ provided their probability total $\leq 1$ |
### Part (d):
| Answer | Mark | Guidance |
|--------|------|----------|
| $p(\text{odd, odd}) + p(\text{even, even})$ soi or $1 - p(\text{odd, even})$ etc | M1 | Can score this mark for the intention to calculate $p(\text{odd, odd}) + p(\text{even, even})$ - may be stated, or partial cases listed, or with a tree diagram with correct pathways or with a statement of 'odd, odd' and 'even, even' and an attempt to add. |
| $\left(\frac{2}{3}\right)^2 + \left(\frac{1}{3}\right)^2$ | A1 | |
| $\frac{5}{9}$ o.e. $\frac{20}{36}$ etc | A1 | allow $0.\dot{5}$ correct to 3 dp or better so $0.555\ldots$ or $0.555$ but not $0.55$ however isw once $\frac{5}{9}$ o.e. seen. Condone $0.556$ |
# Mark Scheme Extraction
## Question (Probability - Sample Space):
**Alternative 1:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Complete sample space diagram (as shown with sums of two dice ranging from 2 to 14) | M1 | 3.1a - Complete sample space diagram with maximum two errors |
| Extraction of even outcomes (underlined values in diagram) | A1 | 2.1 - Extraction of even outcomes - may circle or underline etc. |
| $\frac{5}{9}$ o.e. $\frac{20}{36}$ etc | A1 | 1.1 - Allow $0.\dot{5}$ correct to 3 dp or better so 0.555… or 0.555 but not 0.55 however isw once $\frac{5}{9}$ o.e. seen. Condone 0.556 |
**Alternative 2:**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Listing cases: $(1,3)\ (1,5)\ (1,7)\ (3,5)\ (3,7)\ (4,6)\ (5,7)$ x2 and $(1,1)\ (3,3)\ (4,4)\ (5,5)\ (6,6)\ (7,7)$ | M1 | 3.1a - Must make a clear attempt at pairing odd with odd **and** even with even. List can be incomplete for this mark |
| A complete list extracted | A1 | 2.1 - May be implied by a correct answer |
| $\frac{5}{9}$ o.e. $\frac{20}{36}$ etc | A1 | 1.1 - Allow $0.\dot{5}$ correct to 3 dp or better so 0.555… but not 0.55 however isw once $\frac{5}{9}$ o.e. seen. Condone 0.556 |
**Total: [3]**
---9 A fair six-sided die has its faces numbered 1, 3, 4, 5, 6 and 7. The die is rolled once.\\
$A$ is the event that the die shows an even number.\\
$B$ is the event that the die shows a prime number.
\begin{enumerate}[label=(\alph*)]
\item Write down the value of $\mathrm { p } ( A )$.
\item Write down the value of $\mathrm { p } ( B )$.
\item Write down the value of $\mathrm { p } ( A$ or $B )$.
The die is rolled again.
\item Calculate the probability that the sum of the scores from the two rolls is even.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2024 Q9 [6]}}