| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2020 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Two-way table probabilities |
| Difficulty | Easy -1.3 This is a straightforward probability question requiring only basic counting and probability rules. Parts (a) and (b) involve simple probability calculations from a two-way table (total favorable/total possible), part (c) uses conditional probability with straightforward counting, and part (d) requires combinations but with standard formula application. No problem-solving insight needed—purely routine calculations that any competent A-level student should handle mechanically. |
| Spec | 2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Primary | Secondary | Sixth-form | |
| Male | 9 | 24 | 23 |
| Female | 35 | 85 | 24 |
| Answer | Marks |
|---|---|
| 13(a)(i) | Calculates the correct |
| Answer | Marks | Guidance |
|---|---|---|
| OE | 1.1b | B1 |
| Answer | Marks |
|---|---|
| 13(a)(ii) | Calculates the correct |
| Answer | Marks | Guidance |
|---|---|---|
| rounded to 0.77 or better | 1.1b | B1 |
| Answer | Marks |
|---|---|
| 13(b) | Finds the total male teachers |
| Answer | Marks | Guidance |
|---|---|---|
| 200 | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| AWRT 0.84 | 1.1b | A1 |
| Answer | Marks |
|---|---|
| 13(c) | Finds P(all three secondary |
| Answer | Marks | Guidance |
|---|---|---|
| PI by correct answer | 3.1b | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| incorrect working | 1.1b | A1 |
| Total | 6 |
| Answer | Marks | Guidance |
|---|---|---|
| Q | Marking Instructions | AO |
Question 13:
--- 13(a)(i) ---
13(a)(i) | Calculates the correct
probability
OE | 1.1b | B1 | 18
--- 13(a)(ii) ---
13(a)(ii) | Calculates the correct
probability
OE
Allow value truncated to 0.76 or
rounded to 0.77 or better | 1.1b | B1 | 153
200
--- 13(b) ---
13(b) | Finds the total male teachers
PI if seen or by correct
56
answer
200 | 1.1a | M1 | 9 + 24 + 23 = 56
=
47
56
Obtains the correct probability
OE
AWRT 0.84 | 1.1b | A1
--- 13(c) ---
13(c) | Finds P(all three secondary
teachers)
PI by correct answer | 3.1b | M1 | × ×
109 108 107
200 199 198
= 0.16
Obtains the correct probability
AWRT 0.16
Do not allow 0.16 coming from
incorrect working | 1.1b | A1
Total | 6
9 + 24 + 23 = 56
=
Q | Marking Instructions | AO | Marks | Typical SolutionDiedre is a head teacher in a school which provides primary, secondary and sixth-form education.
There are 200 teachers in her school.
The number of teachers in each level of education along with their gender is shown in the table below.
\begin{tabular}{|l|c|c|c|}
\hline
& Primary & Secondary & Sixth-form \\
\hline
Male & 9 & 24 & 23 \\
\hline
Female & 35 & 85 & 24 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\alph*)]
\item A teacher is selected at random. Find the probability that:
\begin{enumerate}[label=(\roman*)]
\item the teacher is female
[1 mark]
\item the teacher is not a sixth-form teacher.
[1 mark]
\end{enumerate}
\item Given that a randomly chosen teacher is male, find the probability that this teacher is not a primary teacher.
[2 marks]
\item Diedre wants to select three different teachers at random to be part of a school project.
Calculate the probability that all three chosen are secondary teachers.
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2020 Q13 [6]}}