| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Independent Events |
| Type | Independent repeated trials |
| Difficulty | Moderate -0.8 This is a straightforward conditional probability question using basic tree diagram methods. Part (a) requires simple probability multiplication and addition (0.2² + 0.8² = 0.68), while part (b) is a standard 'given that' conditional probability calculation using P(both bronze)/P(at least one bronze). Both parts are routine applications of AS-level probability with no problem-solving insight required, making this easier than average but not trivial due to the two-part structure and conditional probability element. |
| Spec | 2.03c Conditional probability: using diagrams/tables |
| Answer | Marks |
|---|---|
| 13(a) | Finds P(both bronze) or |
| Answer | Marks | Guidance |
|---|---|---|
| PI by correct answer | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| correct probability seen | 1.1b | A1 |
| Subtotal | 2 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 13(b) | Finds P(at least one of the coins | |
| is bronze) | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| correct probability seen | 2.2a | A1 |
| Subtotal | 2 | |
| Question 13 Total | 4 | |
| Q | Marking instructions | AO |
Question 13:
--- 13(a) ---
13(a) | Finds P(both bronze) or
P(both silver)
or calculates 1 – 2 × 0.2 × 0.8
PI by correct answer | 3.1b | M1 | P(both bronze) = 0.2 × 0.2 = 0.04
P(both silver) = 0.8 × 0.8 = 0.64
P(both same type) = 0.68
Obtains the correct probability
Ignore incorrect rounding after
correct probability seen | 1.1b | A1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 13(b) ---
13(b) | Finds P(at least one of the coins
is bronze) | 3.1b | M1 | P(at least one bronze)
= 1 – 0.8 × 0.8
= 0.36
P(both bronze I at least one
bronze)
0.2×0.2 1
= =
0.36 9
Obtains the correct probability
1
Allow 0.11 or better for
9
Ignore incorrect rounding after
correct probability seen | 2.2a | A1
Subtotal | 2
Question 13 Total | 4
Q | Marking instructions | AO | Marks | Typical solutionThere are two types of coins in a money box:
• 20% are bronze coins
• 80% are silver coins
Craig takes out a coin at random and places it back in the money box.
Craig then takes out a second coin at random.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that both coins were of the same type.
[2 marks]
\item Find the probability that both coins are bronze, given that at least one of the coins is bronze.
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2023 Q13 [4]}}