| Exam Board | Edexcel |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2022 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Basic two-way table probability |
| Difficulty | Moderate -0.8 This is a straightforward conditional probability question using a two-way table and Venn diagram. Parts (a)-(b) require simple division from the table, part (c) involves calculating percentages and filling in a Venn diagram, and parts (d)-(f) require basic set operations and conditional probability formulas. All techniques are standard and computational with no novel insight required, making it easier than average. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| \cline { 2 - 3 } \multicolumn{1}{c|}{} | \(\boldsymbol { A }\) | \(\boldsymbol { B }\) |
| Professional | 740 | 380 |
| Skilled | 275 | 90 |
| Elementary | 260 | 80 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{365}{1825}\) or \(\frac{1}{5}\) or 0.2 oe | B1 | Allow equivalent |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{170}{1825}\) or \(\frac{34}{365}\) or awrt 0.093 | B1 | Allow equivalent |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(90\times0.4+80\times0.05[=40]\) or \(90\times0.6+80\times0.95[=130]\) or \(740\times0.65[=481]\) or \(740\times0.35[=259]\) | M1 | Correct method to find one of the values 40 or 130 or 481 or 259. Implied by 40, 481, 259 or 130 seen in correct place on diagram |
| One of the highlighted values correct (40 or 481) | B1 | |
| A second highlighted value correct or their \((259+481)=740\) or their \((40+481)=521\) or their \((40+130)=170\) | B1 | |
| Fully correct diagram | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(P(R'\cap F) = \frac{380}{1825}\left[=\frac{76}{365}=0.208...\right]\) oe awrt 0.208 | B1 | 380/1825 oe or awrt 0.208 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{133+"130"}{1825} = \frac{"263"}{1825}\) awrt 0.144 | B1ft | Correct answer or ft their \(130\ (>0)\). Do not allow if blank. Allow ft correct to 3 sf |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{247+"481"}{247+"481"+123+"40"} = \frac{728}{891}\) awrt 0.817 | M1 | For a single fraction with numerator \(<\) denominator and \(n\) is an integer we will award for \(n/891\) or \(n/(\text{sum of their 4 values in }H,\text{ each}>0)\) or awrt 0.817 |
| A1 | 728/891 oe or awrt 0.817 |
# Question 5:
## Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{365}{1825}$ or $\frac{1}{5}$ or 0.2 oe | B1 | Allow equivalent |
## Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{170}{1825}$ or $\frac{34}{365}$ or awrt 0.093 | B1 | Allow equivalent |
## Part (c):
| Answer | Mark | Guidance |
|--------|------|----------|
| $90\times0.4+80\times0.05[=40]$ or $90\times0.6+80\times0.95[=130]$ or $740\times0.65[=481]$ or $740\times0.35[=259]$ | M1 | Correct method to find one of the values 40 or 130 or 481 or 259. Implied by 40, 481, 259 or 130 seen in correct place on diagram |
| One of the highlighted values correct (40 or 481) | B1 | |
| A second highlighted value correct or their $(259+481)=740$ or their $(40+481)=521$ or their $(40+130)=170$ | B1 | |
| Fully correct diagram | A1 | |
## Part (d):
| Answer | Mark | Guidance |
|--------|------|----------|
| $P(R'\cap F) = \frac{380}{1825}\left[=\frac{76}{365}=0.208...\right]$ oe awrt 0.208 | B1 | 380/1825 oe or awrt 0.208 |
## Part (e):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{133+"130"}{1825} = \frac{"263"}{1825}$ awrt 0.144 | B1ft | Correct answer or ft their $130\ (>0)$. Do not allow if blank. Allow ft correct to 3 sf |
## Part (f):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{247+"481"}{247+"481"+123+"40"} = \frac{728}{891}$ awrt 0.817 | M1 | For a single fraction with numerator $<$ denominator and $n$ is an integer we will award for $n/891$ **or** $n/(\text{sum of their 4 values in }H,\text{ each}>0)$ or awrt 0.817 |
| | A1 | 728/891 oe or awrt 0.817 |
---\begin{enumerate}
\item A company has 1825 employees.
\end{enumerate}
The employees are classified as professional, skilled or elementary.\\
The following table shows
\begin{itemize}
\item the number of employees in each classification
\item the two areas, $A$ or $B$, where the employees live
\end{itemize}
\begin{center}
\begin{tabular}{ | l | c | c | }
\cline { 2 - 3 }
\multicolumn{1}{c|}{} & $\boldsymbol { A }$ & $\boldsymbol { B }$ \\
\hline
Professional & 740 & 380 \\
\hline
Skilled & 275 & 90 \\
\hline
Elementary & 260 & 80 \\
\hline
\end{tabular}
\end{center}
An employee is chosen at random.\\
Find the probability that this employee\\
(a) is skilled,\\
(b) lives in area $B$ and is not a professional.
Some classifications of employees are more likely to work from home.
\begin{itemize}
\item $65 \%$ of professional employees in both area $A$ and area $B$ work from home
\item $40 \%$ of skilled employees in both area $A$ and area $B$ work from home
\item $5 \%$ of elementary employees in both area $A$ and area $B$ work from home
\item Event $F$ is that the employee is a professional
\item Event $H$ is that the employee works from home
\item Event $R$ is that the employee is from area $A$\\
(c) Using this information, complete the Venn diagram on the opposite page.\\
(d) Find $\mathrm { P } \left( R ^ { \prime } \cap F \right)$\\
(e) Find $\mathrm { P } \left( [ H \cup R ] ^ { \prime } \right)$\\
(f) Find $\mathrm { P } ( F \mid H )$
\end{itemize}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{3a09f809-fa28-4b3d-bb69-ea074433bd8f-13_872_1020_294_525}
\end{center}
Turn over for a spare diagram if you need to redraw your Venn diagram.
Only use this diagram if you need to redraw your Venn diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{3a09f809-fa28-4b3d-bb69-ea074433bd8f-15_872_1017_392_525}\\
\hfill \mbox{\textit{Edexcel Paper 3 2022 Q5 [10]}}