| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Standard Survey to Venn Diagram |
| Difficulty | Easy -1.2 This is a straightforward application of the inclusion-exclusion principle with all values provided directly. Students simply fill in a Venn diagram systematically (starting with the intersection of all three, then pairwise intersections, then individual regions) and read off probabilities. It requires careful arithmetic but no problem-solving insight or novel reasoning—purely mechanical execution of a standard S1 technique. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| 3 closed, labelled overlapping curves | M1 | |
| Values 90, 3, 2, 1 correct | A1 | |
| One of 1, 0 or 2 correct or correct sum for \(A\), \(B\) or \(C\) | M1A1 | |
| All 7 values correct (accept blank instead of 0) | A1 | |
| 1 outside box | B1 | Final mark is B1 for box |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(\text{none}) = 0.01\) | B1ft | Follow through their '1' from outside divided by 100 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(A \text{ but not } B) = 0.04\) | M1, A1ft | M1 for correct expression e.g. \(P(A \cup B) - P(B)\); ft their '3+1' from diagram |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(\text{any wine but } C) = 0.03\) | M1, A1ft | M1 for correct expression e.g. \(1+2+0\) or \(99-96\); ft their '2+1+0' |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(\text{exactly two}) = 0.06\) | M1, A1ft | M1 for correct expression e.g. \(3+2+1\) or 6 on top |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(C \mid A) = \frac{P(C \cap A)}{P(A)} = \frac{93}{96} = \frac{31}{32}\) | M1, A1ft, A1 | AWRT 0.969; M1 for correct expression with some correct substitution; if \(P(C)\) on bottom: M0 |
## Question 5:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| 3 closed, labelled overlapping curves | M1 | |
| Values 90, 3, 2, 1 correct | A1 | |
| One of 1, 0 or 2 correct or correct sum for $A$, $B$ or $C$ | M1A1 | |
| All 7 values correct (accept blank instead of 0) | A1 | |
| 1 outside box | B1 | Final mark is B1 for box |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(\text{none}) = 0.01$ | B1ft | Follow through their '1' from outside divided by 100 |
### Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(A \text{ but not } B) = 0.04$ | M1, A1ft | M1 for correct expression e.g. $P(A \cup B) - P(B)$; ft their '3+1' from diagram |
### Part (d)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(\text{any wine but } C) = 0.03$ | M1, A1ft | M1 for correct expression e.g. $1+2+0$ or $99-96$; ft their '2+1+0' |
### Part (e)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(\text{exactly two}) = 0.06$ | M1, A1ft | M1 for correct expression e.g. $3+2+1$ or 6 on top |
### Part (f)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(C \mid A) = \frac{P(C \cap A)}{P(A)} = \frac{93}{96} = \frac{31}{32}$ | M1, A1ft, A1 | AWRT 0.969; M1 for correct expression with some correct substitution; if $P(C)$ on bottom: M0 |5. The following shows the results of a wine tasting survey of 100 people.
\begin{displayquote}
96 like wine $A$,\\
93 like wine $B$,\\
96 like wine $C$,\\
92 like $A$ and $B$,\\
91 like $B$ and $C$,\\
93 like $A$ and $C$,\\
90 like all three wines.
\begin{enumerate}[label=(\alph*)]
\item Draw a Venn Diagram to represent these data.
\end{displayquote}
Find the probability that a randomly selected person from the survey likes
\item none of the three wines,
\item wine $A$ but not wine $B$,
\item any wine in the survey except wine $C$,
\item exactly two of the three kinds of wine.
Given that a person from the survey likes wine $A$,
\item find the probability that the person likes wine $C$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2008 Q5 [16]}}