| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2020 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tree Diagrams |
| Type | Two-stage sampling with replacement |
| Difficulty | Moderate -0.8 Part (a) is a straightforward two-stage probability calculation without replacement using standard combinations or tree diagrams. Part (b) requires conditional probability with two bags but follows a standard textbook pattern (law of total probability). Both parts involve routine probability techniques with clear structure and no novel insight required, making this easier than average for AS-level. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
| Answer | Marks |
|---|---|
| 18(a) | Finds the sum of two or more |
| Answer | Marks | Guidance |
|---|---|---|
| having denominators of 12 and 11 | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| (accept 0.53 or better) | 1.1b | A1 |
| Subtotal | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| 18(b) | Uses correct denominator (12 × 10) | |
| at least once | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| (OE) | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| (accept 0.63 or better) | 1.1b | A1 |
| Subtotal | 3 | |
| Question Total | 5 | |
| Q | Marking Instructions | AO |
Question 18:
--- 18(a) ---
18(a) | Finds the sum of two or more
products each term in the products
having denominators of 12 and 11 | 1.1a | M1 | P(one blue) = +
7 5 5 7
12 × 11 12 × 11
=
35
66
Obtains OE
35
66
(accept 0.53 or better) | 1.1b | A1
Subtotal | 2
--- 18(b) ---
18(b) | Uses correct denominator (12 × 10)
at least once | 1.1b | B1 | P(Red from Bag B)
= +
8 6 4 7
12 × 10 12 × 10
=
19
30
Uses correct numerator in two or
three termed expression
(8×6)+(4×7)
or
(7×6)+(4×7)+(1×6)
(OE) | 1.1a | M1
Obtains OE
19
30
(accept 0.63 or better) | 1.1b | A1
Subtotal | 3
Question Total | 5
Q | Marking Instructions | AO | Marks | Typical Solution\begin{enumerate}[label=(\alph*)]
\item Bag A contains 7 blue discs, 4 red discs and 1 yellow disc.
Two discs are drawn at random from bag A without replacement.
Find the probability that exactly one of the discs is blue.
[2 marks]
\item Bag A contains 7 blue discs, 4 red discs and 1 yellow disc.
Bag B contains 3 blue discs and 6 red discs.
A disc is drawn at random from Bag A and placed in Bag B.
A disc is then drawn at random from Bag B.
Find the probability that the disc drawn from Bag B is red.
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2020 Q18 [5]}}