| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2001 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Basic two-way table probability |
| Difficulty | Easy -1.3 This is a straightforward S1 conditional probability question using a two-way table and basic tree diagram. Parts (a)-(b) require simple probability calculations from the table, part (c) is routine tree diagram construction, part (d) uses the law of total probability with given percentages, and part (e) applies Bayes' theorem in a standard format. All techniques are direct applications of basic formulas with no problem-solving insight required. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Live close |
| |||
| Management | 6 | 14 | ||
| Administration | 25 | 10 | ||
| Production | 45 | 25 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(\text{admin}) = \frac{35}{125} = \frac{7}{25}\) or \(0.28\) | M1 A1 (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(\text{close} \mid \text{Manager}) = \frac{6}{20} = \frac{3}{10}\) or \(0.3\) | M1 A1 (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Tree diagram with correct branches: \(\frac{20}{125}\) Manager, \(\frac{35}{125}\) Admin, \(\frac{70}{125}\) Prod; each with M (\(0.9, 0.6, 0.8\)) and \(\bar{M}\) (\(0.1, 0.4, 0.2\)) branches | M1, A1, A1 (3) | M1 for tree; A1 for \(\frac{20}{125}, \frac{35}{125}, \frac{70}{125}\); A1 all correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(\text{Married}) = \frac{20}{125}\times0.9 + \frac{35}{125}\times0.6 + \frac{70}{125}\times0.8\) | M1 A1 | For Manager M + Admin M + Prod M |
| \(= 0.76\) or \(\frac{19}{25}\) | A1 (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(\text{Prod} \mid \text{Married}) = \dfrac{\frac{70}{125}\times0.8}{0.76}\) | M1 A1 | For use of Bayes' |
| \(= 0.589\) or \(\frac{56}{95}\) or \(0.59\) | A1 (3) |
## Question 4:
**Part (a)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(\text{admin}) = \frac{35}{125} = \frac{7}{25}$ or $0.28$ | M1 A1 (2) | |
**Part (b)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(\text{close} \mid \text{Manager}) = \frac{6}{20} = \frac{3}{10}$ or $0.3$ | M1 A1 (2) | |
**Part (c)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Tree diagram with correct branches: $\frac{20}{125}$ Manager, $\frac{35}{125}$ Admin, $\frac{70}{125}$ Prod; each with M ($0.9, 0.6, 0.8$) and $\bar{M}$ ($0.1, 0.4, 0.2$) branches | M1, A1, A1 (3) | M1 for tree; A1 for $\frac{20}{125}, \frac{35}{125}, \frac{70}{125}$; A1 all correct |
**Part (d)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(\text{Married}) = \frac{20}{125}\times0.9 + \frac{35}{125}\times0.6 + \frac{70}{125}\times0.8$ | M1 A1 | For Manager M + Admin M + Prod M |
| $= 0.76$ or $\frac{19}{25}$ | A1 (3) | |
**Part (e)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(\text{Prod} \mid \text{Married}) = \dfrac{\frac{70}{125}\times0.8}{0.76}$ | M1 A1 | For use of Bayes' |
| $= 0.589$ or $\frac{56}{95}$ or $0.59$ | A1 (3) | |
---4. The employees of a company are classified as management, administration or production. The following table shows the number employed in each category and whether or not they live close to the company or some distance away.
\begin{center}
\begin{tabular}{ | l | c | c | }
\hline
& Live close & \begin{tabular}{ c }
Live some \\
distance away \\
\end{tabular} \\
\hline
Management & 6 & 14 \\
\hline
Administration & 25 & 10 \\
\hline
Production & 45 & 25 \\
\hline
\end{tabular}
\end{center}
An employee is chosen at random.\\
Find the probability that this employee
\begin{enumerate}[label=(\alph*)]
\item is an administrator,
\item lives close to the company, given that the employee is a manager.
Of the managers, $90 \%$ are married, as are $60 \%$ of the administrators and $80 \%$ of the production employees.
\item Construct a tree diagram containing all the probabilities.
\item Find the probability that an employee chosen at random is married.
An employee is selected at random and found to be married.
\item Find the probability that this employee is in production.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2001 Q4 [13]}}