Easy -1.3 This is a straightforward probability question testing basic concepts: reading from a two-way table, finding complements, conditional probability, and independence. All parts require only direct application of standard formulas with no problem-solving insight. The table is already given in probability form, making calculations trivial. This is easier than average A-level content.
The Human Resources director in a company is investigating the graduate status and salaries of its employees.
Event \(G\) is defined as the employee is a graduate.
Event \(H\) is defined as the employee earns at least £40 000 a year.
The director summarised the findings in the table of probabilities below.
\(H\)
\(H'\)
\(G\)
0.21
0.18
\(G'\)
0.07
0.54
\begin{enumerate}[label=(\alph*)]
\item An employee is selected at random.
Find P(\(G\))
[1 mark]
Find P[\((G \cap H)'\)]
[2 marks]
Find P(\(H | G'\))
[2 marks]
\item Determine whether the events \(G\) and \(H\) are independent.
Fully justify your answer.
[2 marks]
Question 18:
--- 18(a)(i) ---
18(a)(i) | Obtains 0.39 | 1.1b | B1 | 0.39
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 18(a)(ii) ---
18(a)(ii) | States or calculates 1 – P(G∩H)
or
states 0.07 + 0.18 + 0.54
PI by correct answer | 1.1a | M1 | 1 – 0.21 = 0.79
Obtains 0.79 | 1.1b | A1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 18(a)(iii) ---
18(a)(iii) | P ( H G) )
States P(H | G/) =
P ( G
Condone missing P(H | G/)
or
states P(H ∩ G/) = 0.07 or
0.07
seen
k
or
states 0.07 + 0.54 or 0.61 or
k
seen
0.07+0.54
PI by correct answer | 1.1a | M1 | P ( H G) )
P(H | G/) =
P ( G
0 .0 7
=
0 .6 1
7
=
61
7
Obtains
6 1
or AWFW [0.11, 0.115] | 1.1b | A1
Subtotal | 2
Q | Marking instructions | AO | Marks | Typical solution
--- 18(b) ---
18(b) | States their P(G) from part
18(a)(i) × 0.28
or
compares their P(G) from part
18(a)(i) with 0.75
or
compares their P(H |G) with
0.28
or
compares their P(H |G/) from
part 18(a)(iii) with 0.28
or any other valid comparison
with one correct probability to at
least 2 sf | 3.1b | M1 | P(G) × P(H) = 0.39 × 0.28
= 0.1092
P(G∩H) = 0.21
P(G∩H) ≠ P(G) × P(H)
Hence G and H are not
independent
Completes a reasoned
argument and concludes that
G and H are not independent | 2.4 | R1
Subtotal | 2
Question 18 Total | 7
Q | Marking instructions | AO | Marks | Typical solution
The Human Resources director in a company is investigating the graduate status and salaries of its employees.
Event $G$ is defined as the employee is a graduate.
Event $H$ is defined as the employee earns at least £40 000 a year.
The director summarised the findings in the table of probabilities below.
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
& $H$ & $H'$ \\
\hline
$G$ & 0.21 & 0.18 \\
\hline
$G'$ & 0.07 & 0.54 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item An employee is selected at random.
\begin{enumerate}[label=(\roman*)]
\item Find P($G$)
[1 mark]
\item Find P[$(G \cap H)'$]
[2 marks]
\item Find P($H | G'$)
[2 marks]
\end{enumerate}
\item Determine whether the events $G$ and $H$ are independent.
Fully justify your answer.
[2 marks]
</end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2024 Q18 [7]}}