| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Independence test requiring preliminary calculations |
| Difficulty | Moderate -0.8 This is a straightforward probability question testing basic concepts of independence and the addition rule. Part (a) requires simple calculation of P(A)P(B) vs P(A∩B) using given frequencies. Part (b) applies the standard formula P(A∪B) = P(A) + P(B) - P(A∩B) where P(A∩B) is found from conditional probability. Both parts are routine applications of textbook formulas with no problem-solving insight required, making this easier than average. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables |
| Answer | Marks |
|---|---|
| 14(a) | Calculates |
| Answer | Marks |
|---|---|
| P(studies Geography | studiesPhysics) |
| Answer | Marks | Guidance |
|---|---|---|
| P(studies Physics | studiesGeography) | AO3.1b |
| Answer | Marks | Guidance |
|---|---|---|
| independent | AO2.1 | R1 |
| Answer | Marks | Guidance |
|---|---|---|
| 14(b) | Uses conditional probability to | |
| calculate | AO3.1b | M1 |
| 𝑃𝑃(𝑀𝑀∩𝐵𝐵) 𝑃𝑃(𝑀𝑀)×𝑃𝑃(𝐵𝐵 | 𝑀𝑀 ) |
| Answer | Marks | Guidance |
|---|---|---|
| 𝑃𝑃(𝑀𝑀∩𝐵𝐵) | AO1.1b | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 𝑃𝑃(𝑀𝑀∩𝐵𝐵) | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| 𝑃𝑃(𝑀𝑀∪𝐵𝐵) | AO1.1b | A1 |
Total
| Answer | Marks | Guidance |
|---|---|---|
| 𝑃𝑃(𝑀𝑀∪𝐵𝐵) | 6 | = |
| Answer | Marks | Guidance |
|---|---|---|
| Q | Marking Instructions | AO |
Question 14:
--- 14(a) ---
14(a) | Calculates
P(studiesPhysics)×P(studiesGeography)
or
Calculates
P(studies Geography|studiesPhysics)
or
P(studies Physics|studiesGeography) | AO3.1b | M1 | 12 8 1
P(P)×P(G)= × =
24 24 6
4 1
P(P∩G)= =
24 6
Hence P(P)×P(G)= P(P∩G)
Therefore events are independent
Shows
P(studiesPhysics)×P(studiesGeography)
=P(studiesPhysics∩studiesGeography)
and correctly concludes that the
events are independent
or
Shows that the appropriate
conditional probability is equal to
P(studiesGeography) or
P(studiesPhysics) and correctly
concludes that the events are
independent | AO2.1 | R1
--- 14(b) ---
14(b) | Uses conditional probability to
calculate | AO3.1b | M1 | =
𝑃𝑃(𝑀𝑀∩𝐵𝐵) 𝑃𝑃(𝑀𝑀)×𝑃𝑃(𝐵𝐵|𝑀𝑀 )
1 3 3
= × =
5 8 40
𝑃𝑃(𝑀𝑀)+𝑃𝑃(𝐵𝐵)−𝑃𝑃(𝑀𝑀∩𝐵𝐵 )
1 1 3
= + −
5 6 40
7
Obtains the correct value of
𝑃𝑃(𝑀𝑀∩𝐵𝐵) | AO1.1b | A1
Uses the addition rule to calculate
𝑃𝑃(𝑀𝑀∩𝐵𝐵) | AO1.1a | M1
Obtains the correct value of
𝑃𝑃(𝑀𝑀∪𝐵𝐵) | AO1.1b | A1
Total
𝑃𝑃(𝑀𝑀∪𝐵𝐵) | 6 | =
24
Q | Marking Instructions | AO | Marks | Typical SolutionA teacher in a college asks her mathematics students what other subjects they are studying.
She finds that, of her 24 students:
12 study physics
8 study geography
4 study geography and physics
\begin{enumerate}[label=(\alph*)]
\item A student is chosen at random from the class.
Determine whether the event 'the student studies physics' and the event 'the student studies geography' are independent.
[2 marks]
\item It is known that for the whole college:
the probability of a student studying mathematics is $\frac{1}{5}$
the probability of a student studying biology is $\frac{1}{6}$
the probability of a student studying biology given that they study mathematics is $\frac{3}{8}$
Calculate the probability that a student studies mathematics or biology or both.
[4 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2018 Q14 [6]}}