| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Given conditional, find joint or marginal |
| Difficulty | Standard +0.3 This is a standard S1 conditional probability question requiring systematic application of probability rules (conditional probability formula, De Morgan's laws, independence, mutual exclusivity) across multiple parts. While it has several steps and requires careful bookkeeping, each individual technique is routine for A-level statistics, making it slightly easier than average overall. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(A\cap B)=0.4\) | B1 | |
| \(P(A\mid B)=\dfrac{0.4}{P(B)}=\dfrac{2}{3}\) | M1 | \(\frac{\text{their }0.4}{P(B)}=\frac{2}{3}\); use of \(P(A\cap B)=P(A)\times P(B)\) is M0 |
| \(P(B)=0.6\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(A'\mid B')=\dfrac{0.5+\text{'0.4'}-\text{'0.6'}}{1-\text{'0.6'}}=\dfrac{3}{4}\) | M1 A1 | M1 for \(\frac{0.5+\text{their }P(A\cap B)-\text{their (a)}}{1-\text{their (a)}}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(B\cap C)=\text{'0.6'}\times0.15=0.09\) | M1 A1 | M1 their (a) \(\times0.15\), \(0<\) their (a) \(<1\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 3 circles labelled A, B, C with B intersecting A and C, and \(P(A\cap C)=0\) | M1 | Do not allow blanks as 0s |
| 0.09 and 0.06 or their (c) and \(0.15-\) their (c) | M1 | |
| 0.4 and 0.1 or probabilities in A such that \(P(A)=0.5\) | M1 | |
| 0.11 and 0.24 or all 6 probs add to 1 and probs in B such that \(P(B)=\text{'0.6'}\) | A1ft | dep on 1st M1 |
| All correct with box: 0.1, 0.4, 0.11, 0.09, 0.06, 0.24 | A1 | NOTE: No labels allow access to 2nd and 3rd M1 marks ONLY |
# Question 7:
## Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(A\cap B)=0.4$ | B1 | |
| $P(A\mid B)=\dfrac{0.4}{P(B)}=\dfrac{2}{3}$ | M1 | $\frac{\text{their }0.4}{P(B)}=\frac{2}{3}$; use of $P(A\cap B)=P(A)\times P(B)$ is M0 |
| $P(B)=0.6$ | A1 | |
## Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(A'\mid B')=\dfrac{0.5+\text{'0.4'}-\text{'0.6'}}{1-\text{'0.6'}}=\dfrac{3}{4}$ | M1 A1 | M1 for $\frac{0.5+\text{their }P(A\cap B)-\text{their (a)}}{1-\text{their (a)}}$ |
## Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(B\cap C)=\text{'0.6'}\times0.15=0.09$ | M1 A1 | M1 their (a) $\times0.15$, $0<$ their (a) $<1$ |
## Part (d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| 3 circles labelled A, B, C with B intersecting A and C, and $P(A\cap C)=0$ | M1 | Do not allow blanks as 0s |
| 0.09 and 0.06 or their (c) and $0.15-$ their (c) | M1 | |
| 0.4 and 0.1 or probabilities in A such that $P(A)=0.5$ | M1 | |
| 0.11 and 0.24 or all 6 probs add to 1 and probs in B such that $P(B)=\text{'0.6'}$ | A1ft | dep on 1st M1 |
| All correct with box: 0.1, 0.4, 0.11, 0.09, 0.06, 0.24 | A1 | NOTE: No labels allow access to 2nd and 3rd M1 marks ONLY |
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This appears to be a back cover or blank page from a Pearson mark scheme document. Could you share the pages that actually contain the mark scheme questions and answers?\begin{enumerate}
\item Events $A$ and $B$ are such that
\end{enumerate}
$$\mathrm { P } ( A ) = 0.5 \quad \mathrm { P } ( A \mid B ) = \frac { 2 } { 3 } \quad \mathrm { P } \left( A ^ { \prime } \cup B ^ { \prime } \right) = 0.6$$
(a) Find $\mathrm { P } ( B )$\\
(b) Find $\mathrm { P } \left( A ^ { \prime } \mid B ^ { \prime } \right)$
The event $C$ has $\mathrm { P } ( C ) = 0.15$
The events $A$ and $C$ are mutually exclusive.
The events $B$ and $C$ are independent.\\
(c) Find $\mathrm { P } ( B \cap C )$\\
(d) Draw a Venn diagram to illustrate the events $A , B$ and $C$ and the probabilities for each region.\\
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\hfill \mbox{\textit{Edexcel S1 2018 Q7 [12]}}