| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Venn diagram with two events |
| Difficulty | Moderate -0.8 This is a straightforward conditional probability question requiring basic application of P(A∩B) = P(A)P(B|A), constructing a standard Venn diagram with given probabilities, and reading off simple union/complement probabilities. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial due to the multi-part structure. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(P(\text{jacket and tie}) = 0.4 \times 0.3 = 0.12\) | M1, A1 CAO | M1 for multiplying |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Venn diagram with two intersecting circles labelled | G1 | G1 for two intersecting circles labelled |
| Values \(0.12\) and either \(0.28\) or \(0.08\) | G1 | |
| All remaining probabilities correct: \(0.28, 0.12, 0.08, 0.52\) | G1 | Note FT their \(0.12\) provided \(< 0.2\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| (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) \(P(\text{no jacket or no tie}) = 0.52 + 0.28 + 0.08 = 0.88\) OR \(0.6 + 0.8 - 0.52 = 0.88\) OR \(1 - 0.12 = 0.88\) | B2 FT | Note FT their \(0.12\) provided \(< 0.2\) |
# Question 5:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(\text{jacket and tie}) = 0.4 \times 0.3 = 0.12$ | M1, A1 CAO | M1 for multiplying |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Venn diagram with two intersecting circles labelled | G1 | G1 for two intersecting circles labelled |
| Values $0.12$ and either $0.28$ or $0.08$ | G1 | |
| All remaining probabilities correct: $0.28, 0.12, 0.08, 0.52$ | G1 | Note FT their $0.12$ provided $< 0.2$ |
## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| (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) $P(\text{no jacket or no tie}) = 0.52 + 0.28 + 0.08 = 0.88$ OR $0.6 + 0.8 - 0.52 = 0.88$ OR $1 - 0.12 = 0.88$ | B2 FT | Note FT their $0.12$ provided $< 0.2$ |
---5 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 2007 Q5 [8]}}