| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2019 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Basic two-way table probability |
| Difficulty | Easy -1.3 This is a straightforward probability question requiring only basic counting and division from a contingency table. Part (a) involves simple probability calculations (10/120, 12/120, 38/50), part (b) requires understanding that events aren't mutually exclusive if they can occur together—all are routine applications of GCSE/AS-level probability concepts with no problem-solving or novel insight required. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Low exercise | Medium exercise | High exercise | |
| Back trouble | 14 | 7 | 10 |
| Stress | 38 | 14 | 5 |
| Depression | 9 | 2 | 1 |
| Headache/Migraine | 4 | 5 | 5 |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(i) | Finds correct probability | |
| OE | 1.1b | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| (a)(ii) | Finds total number for ‘depression’ | 1.1a |
| Answer | Marks | Guidance |
|---|---|---|
| OE | 1.1b | A1 |
| Answer | Marks |
|---|---|
| (a)(iii) | Uses conditional probability to |
| Answer | Marks | Guidance |
|---|---|---|
| 38 | 1.1a | M1 |
| Answer | Marks |
|---|---|
| P(stress | low exercise) to obtain39≤𝑥𝑥≤119 |
| Answer | Marks | Guidance |
|---|---|---|
| ACF | 3.1b | A1 |
| Answer | Marks |
|---|---|
| 14(b) | Shows that 14+38 or 52 |
| Answer | Marks | Guidance |
|---|---|---|
| 50 50 | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| mutually exclusive | 2.4 | R1 |
| Total | 7 | |
| Q | Marking Instructions | AO |
Question 14:
--- 14
(a)(i) ---
14
(a)(i) | Finds correct probability
OE | 1.1b | B1 | 10
--- 14
(a)(ii) ---
14
(a)(ii) | Finds total number for ‘depression’ | 1.1a | M1 | 1 20
9 + 2 + 1 = 12
12
Calculates correct probability
OE | 1.1b | A1
--- 14
(a)(iii) ---
14
(a)(iii) | Uses conditional probability to
calculate
38 | 1.1a | M1 | 120
38
50
P(stress|low exercise) to obtain39≤𝑥𝑥≤119
Obtains correct probability
ACF | 3.1b | A1
--- 14(b) ---
14(b) | Shows that 14+38 or 52
or
14 38
+
50 50 | 3.1b | M1 | 14 + 38 = 52
52 > 50
so events are not mutually
exclusive
Compares 14+38 with 50
or
compares
14 38
+ with 1
50 50
and concludes events are not
mutually exclusive | 2.4 | R1
Total | 7
Q | Marking Instructions | AO | Mark | Typical SolutionA survey was conducted into the health of 120 teachers.
The survey recorded whether or not they had suffered from a range of four health issues in the past year.
In addition, their physical exercise level was categorised as low, medium or high.
50 teachers had a low exercise level, 40 teachers had a medium exercise level and 30 teachers had a high exercise level.
The results of the survey are shown in the table below.
\begin{tabular}{|l|c|c|c|}
\hline
& Low exercise & Medium exercise & High exercise \\
\hline
Back trouble & 14 & 7 & 10 \\
\hline
Stress & 38 & 14 & 5 \\
\hline
Depression & 9 & 2 & 1 \\
\hline
Headache/Migraine & 4 & 5 & 5 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item Find the probability that a randomly selected teacher:
\begin{enumerate}[label=(\roman*)]
\item suffers from back trouble and has a high exercise level; [1 mark]
\item suffers from depression. [2 marks]
\item suffers from stress, given that they have a low exercise level. [2 marks]
\end{enumerate}
\item For teachers in the survey with a low exercise level, explain why the events 'suffers from back trouble' and 'suffers from stress' are not mutually exclusive. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2019 Q14 [7]}}