| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Session | Specimen |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Multi-item selection from population |
| Difficulty | Moderate -0.3 This is a straightforward probability calculation requiring students to find the probability of selecting three specific items from different categories. The calculation is (80/225) × (75/224) × (70/223) × 3!, which involves basic multiplication and understanding that order matters (hence the ×6). While it requires careful arithmetic and recognition of the permutation factor, it's a standard AS-level probability question with no conceptual difficulty beyond the syllabus expectations. |
| Spec | 2.03a Mutually exclusive and independent events |
| Ride written about | ||||
| The Drop | The Beanstalk | The Giant | Total | |
| Year 7 | 24 | 45 | 23 | 92 |
| Year 8 | 36 | 17 | 22 | 75 |
| Year 9 | 20 | 13 | 25 | 58 |
| Total | 80 | 75 | 70 | 225 |
| Answer | Marks | Guidance |
|---|---|---|
| 15 | Finds P(Drop and Beanstalk and | |
| Giant) | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| answer | AO1.1b | A1 |
| Answer | Marks |
|---|---|
| Total | 2 |
Question 15:
15 | Finds P(Drop and Beanstalk and
Giant) | AO1.1a | M1
80 75 70
× ×
225 224 223
Multiplies by 6 to obtain correct
answer | AO1.1b | A1 | 80 75 70
× × ×6=0.224
225 224 223
Total | 2A school took 225 children on a trip to a theme park.
After the trip the children had to write about their favourite ride at the park from a choice of three.
The table shows the number of children who wrote about each ride.
\begin{center}
\begin{tabular}{|c|c|c|c|c|}
\hline
& \multicolumn{3}{|c|}{Ride written about} & \\
\hline
& The Drop & The Beanstalk & The Giant & Total \\
\hline
Year 7 & 24 & 45 & 23 & 92 \\
\hline
Year 8 & 36 & 17 & 22 & 75 \\
\hline
Year 9 & 20 & 13 & 25 & 58 \\
\hline
Total & 80 & 75 & 70 & 225 \\
\hline
\end{tabular}
\end{center}
Three children were randomly selected from those who went on the trip.
Calculate the probability that one wrote about 'The Drop', one wrote about 'The Beanstalk' and one wrote about The Giant'.
[2 marks]
\hfill \mbox{\textit{AQA AS Paper 2 Q15 [2]}}