| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Given conditional, find joint or marginal |
| Difficulty | Moderate -0.8 This is a straightforward conditional probability question requiring basic application of P(A∩B) = P(A)P(B|A), followed by routine Venn diagram construction and simple probability calculations. All steps are standard textbook exercises with no problem-solving insight needed. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
| Answer | Marks | Guidance |
|---|---|---|
| \(P(\text{jacket and tie}) = 0.4 \times 0.3 = 0.12\) | M1 for multiplying, A1 CAO | 2 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Venn diagram with two intersecting circles labelled Jacket and Tie, containing values: 0.28 (Jacket only), 0.12 (intersection), 0.08 (Tie only), 0.52 (outside) | G1 for two intersecting circles labelled; G1 for 0.12 and either 0.28 or 0.08; G1 for remaining probabilities | Note: FT their 0.12 provided \(< 0.2\); 3 marks |
| Answer | Marks |
|---|---|
| OR \(= 0.28 + 0.12 + 0.08 = 0.48\) | B1 FT |
| Answer | Marks | Guidance |
|---|---|---|
| OR \(1 - 0.12 = 0.88\) | B2 FT | Note: FT their 0.12 provided \(< 0.2\); 3 marks |
# Question 2:
## Part (i)
$P(\text{jacket and tie}) = 0.4 \times 0.3 = 0.12$ | M1 for multiplying, A1 CAO | 2 marks
## Part (ii)
Venn diagram with two intersecting circles labelled Jacket and Tie, containing values: 0.28 (Jacket only), 0.12 (intersection), 0.08 (Tie only), 0.52 (outside) | G1 for two intersecting circles labelled; G1 for 0.12 and either 0.28 or 0.08; G1 for remaining probabilities | Note: FT their 0.12 provided $< 0.2$; 3 marks
## Part (iii)
**(A)** $P(\text{jacket or tie}) = P(J) + P(T) - P(J \cap T)$
$= 0.4 + 0.2 - 0.12 = 0.48$
OR $= 0.28 + 0.12 + 0.08 = 0.48$ | B1 FT |
**(B)** $P(\text{no jacket or no tie}) = 0.52 + 0.28 + 0.08 = 0.8$
OR $0.6 + 0.8 - 0.52 = 0.88$
OR $1 - 0.12 = 0.88$ | B2 FT | Note: FT their 0.12 provided $< 0.2$; 3 marks
---2 Each day the probability that Ashwin wears a tie is 0.2 . The probability that he wears a jacket is 0.4 . If he wears a jacket, the probability that he wears a tie is 0.3 .
\begin{enumerate}[label=(\roman*)]
\item Find the probability that, on a randomly selected day, Ashwin wears a jacket and a tie.
\item Draw a Venn diagram, using one circle for the event 'wears a jacket' and one circle for the event 'wears a tie'. Your diagram should include the probability for each region.
\item Using your Venn diagram, or otherwise, find the probability that, on a randomly selected day, Ashwin\\
(A) wears either a jacket or a tie (or both),\\
(B) wears no tie or no jacket (or wears neither).
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 Q2 [8]}}