| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2014 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Principle of Inclusion/Exclusion |
| Type | Constrained Survey to Venn Diagram |
| Difficulty | Standard +0.3 This is a straightforward Venn diagram problem requiring careful reading and systematic placement of values. While it involves multiple constraints, the logic is step-by-step with no conceptual difficulty—students must translate verbal conditions into regions (e.g., folk⊂rock, rock∩soul=∅) and perform basic arithmetic. The conditional probability in part (f) is standard. Slightly above average due to the multiple constraints requiring careful tracking, but well within typical S1 scope. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 3 labelled loops and a box drawn | B1 | 33 not required for any marks in (a) |
| \(F \subset R\) or indicated by zeros | B1 | |
| 30 and 12 correctly placed; \(n(F)=30\) and \(n(F' \cap R)=12\) | B1 | |
| \(S\) a separate loop or indicated by zeros, and 25 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(F\) and \(S\) or \(R\) and \(S\) | B1 | If more than one pair given, each pair must be correct; do not allow \(P(F)\) etc or e.g. \(P(R \cap S)=0\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P([F \cup R \cup S]') = \frac{33}{100}\) or \(\mathbf{0.33}\) | B1 | cao; accept exact equivalent fractions or decimals |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(R) = \frac{30+12}{100} = \frac{21}{50}\) or \(\mathbf{0.42}\) | B1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(F \cup S) = \frac{30+25}{100} = \frac{11}{20}\) or \(\mathbf{0.55}\) | B1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(F\mid R) = \frac{P(F \cap R)}{P(R)} = \frac{"0.30"}{{"0.42"}}\) | M1 | ft their "30" and answer to (d); correct ratio of their probabilities; if num \(>\) den score M0 |
| \(= \frac{30}{42}\) or \(\frac{5}{7}\) (o.e.) | A1 | Must be proper fraction; \(\frac{0.3}{0.42} = 0.714\) is A0; condone \(P(R\mid F) = \frac{30}{42}\) for M1A1 |
# Question 5:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| 3 labelled loops and a box drawn | B1 | 33 not required for any marks in (a) |
| $F \subset R$ or indicated by zeros | B1 | |
| 30 and 12 correctly placed; $n(F)=30$ and $n(F' \cap R)=12$ | B1 | |
| $S$ a separate loop or indicated by zeros, and 25 | B1 | |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $F$ and $S$ or $R$ and $S$ | B1 | If more than one pair given, each pair must be correct; do not allow $P(F)$ etc or e.g. $P(R \cap S)=0$ |
## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P([F \cup R \cup S]') = \frac{33}{100}$ or $\mathbf{0.33}$ | B1 | cao; accept exact equivalent fractions or decimals |
## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(R) = \frac{30+12}{100} = \frac{21}{50}$ or $\mathbf{0.42}$ | B1 | cao |
## Part (e)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(F \cup S) = \frac{30+25}{100} = \frac{11}{20}$ or $\mathbf{0.55}$ | B1 | cao |
## Part (f)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(F\mid R) = \frac{P(F \cap R)}{P(R)} = \frac{"0.30"}{{"0.42"}}$ | M1 | ft their "30" and answer to (d); correct ratio of their probabilities; if num $>$ den score M0 |
| $= \frac{30}{42}$ or $\frac{5}{7}$ (o.e.) | A1 | Must be proper fraction; $\frac{0.3}{0.42} = 0.714$ is A0; condone $P(R\mid F) = \frac{30}{42}$ for M1A1 |
---5. A group of 100 students are asked if they like folk music, rock music or soul music.
\begin{displayquote}
All students who like folk music also like rock music No students like both rock music and soul music 75 students do not like soul music 12 students who like rock music do not like folk music 30 students like folk music
\begin{enumerate}[label=(\alph*)]
\item Draw a Venn diagram to illustrate this information.
\item State two of these types of music that are mutually exclusive.
\end{displayquote}
Find the probability that a randomly chosen student
\item does not like folk music, rock music or soul music,
\item likes rock music,
\item likes folk music or soul music.
Given that a randomly chosen student likes rock music,
\item find the probability that he or she also likes folk music.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2014 Q5 [10]}}