| Exam Board | OCR |
|---|---|
| Module | S4 (Statistics 4) |
| Year | 2010 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Given conditional, find joint or marginal |
| Difficulty | Standard +0.3 This is a straightforward conditional probability question requiring systematic application of standard formulas (P(A|B) = P(A∩B)/P(B)) and set theory laws. Part (i) involves basic manipulation to find P(L) and then applying De Morgan's laws. Part (ii) extends this with one additional step. While it requires careful bookkeeping across multiple parts, it demands no novel insight—just methodical application of A-level formulas, making it slightly easier than average. |
| Spec | 2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(L \cap M) = P(L \mid M)P(M) = 0.12\) and \(P(L) = P(M \cap L)/P(M \mid L) = 0.12/0.4 = 0.3\) | M1, A1 | |
| \(P(L' \cup M') = P[(L \cap M)'] = 1 - P(L \cap M) = 1 - 0.2 \times 0.6 = 0.88\) | B1 [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(N \mid L \cap M) = 0.3\) | M1 | |
| \(\Rightarrow P(N \cap L \cap M) = 0.3 \times 0.12 = 0.036\) | A1 | |
| \(P(L' \cup M' \cup N') = 1 - 0.036 = 0.964\) | A1 [3] |
## Question 8:
### Part (i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(L \cap M) = P(L \mid M)P(M) = 0.12$ and $P(L) = P(M \cap L)/P(M \mid L) = 0.12/0.4 = 0.3$ | M1, A1 | |
| $P(L' \cup M') = P[(L \cap M)'] = 1 - P(L \cap M) = 1 - 0.2 \times 0.6 = 0.88$ | B1 **[3]** | |
### Part (ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(N \mid L \cap M) = 0.3$ | M1 | |
| $\Rightarrow P(N \cap L \cap M) = 0.3 \times 0.12 = 0.036$ | A1 | |
| $P(L' \cup M' \cup N') = 1 - 0.036 = 0.964$ | A1 **[3]** | |8 For the events $L$ and $M , \mathrm { P } ( L \mid M ) = 0.2 , \mathrm { P } ( M \mid L ) = 0.4$ and $\mathrm { P } ( M ) = 0.6$.\\
(i) Find $\mathrm { P } ( L )$ and $\mathrm { P } \left( L ^ { \prime } \cup M ^ { \prime } \right)$.\\
(ii) Given that, for the event $N , \mathrm { P } ( N \mid ( L \cap M ) ) = 0.3$, find $\mathrm { P } \left( L ^ { \prime } \cup M ^ { \prime } \cup N ^ { \prime } \right)$.
\hfill \mbox{\textit{OCR S4 2010 Q8 [6]}}