| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Combined event algebra |
| Difficulty | Moderate -0.3 This is a standard S1 probability question testing basic definitions (mutual exclusivity, independence, conditional probability) and Venn diagrams. Part (b) requires simple algebraic manipulation of P(A∪B) = P(A) + P(B) - P(A∩B) with independence, while other parts are direct applications of formulas. Slightly easier than average due to straightforward application of standard results with no conceptual challenges. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(A \cup C) = \frac{9}{10}\) oe | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(A \cup B) = P(A) + P(B) - P(A) \times P(B)\) | M1 | For use of \(P(A \cup B) = P(A) + P(B) - P(A \cap B)\) |
| \(\frac{5}{8} = \frac{2}{5} + P(B) - \frac{2}{5}P(B)\) | M1 A1 | Second M1: for use of \(P(A \cap B) = P(A) \times P(B)\); just seeing \(\frac{2}{5} \times \frac{3}{8} = \frac{3}{20}\) alone is M0M0 |
| \(P(B) = \frac{3}{8}\) | A1cso | No wrong working seen; allow full verification method |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(A \mid B) = P(A) = \frac{2}{5}\) oe | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Correct Venn diagram (3 circles, \(A\) does not intersect \(C\)) | B1 | At least 2 circles labelled; two zeros shown where \(A\) and \(C\) would intersect |
| \(0.15\) and \(0.25\) placed correctly | M1 | \(0.15\) in \((A \cap B \cap C')\) and \(0.25\) in \((A \cap B' \cap C')\) |
| \(0.05\) and \(0.05\) placed correctly | M1 | \(0.3 -\) (their \(0.25\)) and \(1 -\) (their \(0.15\) + their \(0.25\) + their \(0.05\) + \(\frac{1}{2}\)) |
| \(0.175\) and \(0.325\) placed correctly | M1 A1 | \(\frac{3}{8} -\) (their \(0.15\) + their \(0.05\)) and \(\frac{1}{2} -\) their \(0.175\); fully correct with box |
## Question 6:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(A \cup C) = \frac{9}{10}$ oe | B1 | |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(A \cup B) = P(A) + P(B) - P(A) \times P(B)$ | M1 | For use of $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ |
| $\frac{5}{8} = \frac{2}{5} + P(B) - \frac{2}{5}P(B)$ | M1 A1 | Second M1: for use of $P(A \cap B) = P(A) \times P(B)$; just seeing $\frac{2}{5} \times \frac{3}{8} = \frac{3}{20}$ alone is M0M0 |
| $P(B) = \frac{3}{8}$ | A1cso | No wrong working seen; allow full verification method |
### Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(A \mid B) = P(A) = \frac{2}{5}$ oe | B1 | |
### Part (d):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Correct Venn diagram (3 circles, $A$ does not intersect $C$) | B1 | At least 2 circles labelled; two zeros shown where $A$ and $C$ would intersect |
| $0.15$ and $0.25$ placed correctly | M1 | $0.15$ in $(A \cap B \cap C')$ and $0.25$ in $(A \cap B' \cap C')$ |
| $0.05$ and $0.05$ placed correctly | M1 | $0.3 -$ (their $0.25$) and $1 -$ (their $0.15$ + their $0.25$ + their $0.05$ + $\frac{1}{2}$) |
| $0.175$ and $0.325$ placed correctly | M1 A1 | $\frac{3}{8} -$ (their $0.15$ + their $0.05$) and $\frac{1}{2} -$ their $0.175$; fully correct with box |
---6. Three events $A , B$ and $C$ are such that
$$\mathrm { P } ( A ) = \frac { 2 } { 5 } \quad \mathrm { P } ( C ) = \frac { 1 } { 2 } \quad \mathrm { P } ( A \cup B ) = \frac { 5 } { 8 }$$
Given that $A$ and $C$ are mutually exclusive find
\begin{enumerate}[label=(\alph*)]
\item $\mathrm { P } ( A \cup C )$
Given that $A$ and $B$ are independent
\item show that $\mathrm { P } ( B ) = \frac { 3 } { 8 }$
\item Find $\mathrm { P } ( A \mid B )$
Given that $\mathrm { P } \left( C ^ { \prime } \cap B ^ { \prime } \right) = 0.3$
\item draw a Venn diagram to represent the events $A , B$ and $C$\\
\includegraphics[max width=\textwidth, alt={}, center]{b7500cc1-caa6-4767-bb2e-e3d70474e805-21_2260_53_312_33}
$\_\_\_\_$ VAYV SIHI NI JIIIM ION OC\\
VJYV SIHI NI JIIIM ION OC\\
VJYV SIHI NI JLIYM ION OC
\begin{center}
\end{center}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2018 Q6 [11]}}