| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Constrained Survey to Venn Diagram |
| Difficulty | Easy -1.2 This is a straightforward S1 question requiring students to translate given data into a Venn diagram and perform basic probability calculations. All regions are explicitly stated (no deduction needed), and parts (b)-(d) involve simple counting and division. The conditional probability in (c) is conceptually basic. This is easier than average A-level content. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Blood contains | No. of Patients |
| only \(C\) | 100 |
| \(A\) and \(C\) but not \(B\) | 100 |
| only A | 30 |
| \(B\) and \(C\) but not \(A\) | 25 |
| only \(B\) | 12 |
| \(A , B\) and \(C\) | 10 |
| \(A\) and \(B\) but not \(C\) | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| 3 closed intersecting curves with labels | M1 | |
| Values 100, 100, 30, 12 in correct regions | A1 | |
| Values 10, 3, 25 in correct regions | A1 | |
| Box (with 20 outside all circles) | B1 | 20 not required for diagram mark |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(\text{Substance } C) = \dfrac{100+100+10+25}{300} = \dfrac{235}{300} = \dfrac{47}{60}\) | M1A1ft | M1 for adding values in \(C\) and finding probability |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(\text{All 3} \mid A) = \dfrac{10}{30+3+10+100} = \dfrac{10}{143}\) | M1A1ft | M1 for their 10 divided by their sum of values in \(A\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(\text{Universal donor}) = \dfrac{20}{300} = \dfrac{1}{15}\) | M1A1 cao | M1 for 'their 20' divided by 300 |
## Question 5:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| 3 closed intersecting curves with labels | M1 | |
| Values 100, 100, 30, 12 in correct regions | A1 | |
| Values 10, 3, 25 in correct regions | A1 | |
| Box (with 20 outside all circles) | B1 | 20 not required for diagram mark |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(\text{Substance } C) = \dfrac{100+100+10+25}{300} = \dfrac{235}{300} = \dfrac{47}{60}$ | M1A1ft | M1 for adding values in $C$ and finding probability |
### Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(\text{All 3} \mid A) = \dfrac{10}{30+3+10+100} = \dfrac{10}{143}$ | M1A1ft | M1 for their 10 divided by their sum of values in $A$ |
### Part (d)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(\text{Universal donor}) = \dfrac{20}{300} = \dfrac{1}{15}$ | M1A1 cao | M1 for 'their 20' divided by 300 |5. A person's blood group is determined by whether or not it contains any of 3 substances $A , B$ and $C$.
A doctor surveyed 300 patients' blood and produced the table below.
\begin{center}
\begin{tabular}{|l|l|}
\hline
Blood contains & No. of Patients \\
\hline
only $C$ & 100 \\
\hline
$A$ and $C$ but not $B$ & 100 \\
\hline
only A & 30 \\
\hline
$B$ and $C$ but not $A$ & 25 \\
\hline
only $B$ & 12 \\
\hline
$A , B$ and $C$ & 10 \\
\hline
$A$ and $B$ but not $C$ & 3 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Draw a Venn diagram to represent this information.
\item Find the probability that a randomly chosen patient's blood contains substance $C$.
Harry is one of the patients. Given that his blood contains substance $A$,
\item find the probability that his blood contains all 3 substances.
Patients whose blood contains none of these substances are called universal blood donors.
\item Find the probability that a randomly chosen patient is a universal blood donor.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2008 Q5 [10]}}