| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tree Diagrams |
| Type | Sequential dependent events |
| Difficulty | Moderate -0.8 This is a straightforward conditional probability question using tree diagrams with clear setup and standard calculations. Part (i) is direct reading from the tree, part (ii) requires simple probability addition, and part (iii) involves basic combination of branches. The dependent event structure is explicitly stated, making it easier than average A-level questions that require more problem-solving or insight. |
| Spec | 2.03a Mutually exclusive and independent events2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| 2(i) | \(^4/_7\) or \(0.571\) (3 sfs) | B1: 1 |
| 2(ii) | \(^1/_6 \times ^4/_7 + ^1/_6 \times ^3/_6\) | M1M1: — |
| \(= ^{265}_{448}\) or \(0.592\) (3 sfs) | A1: 3 | |
| 2(iii) | \(^1/_6 \times ^3/_6 + ^5/_6 \times ^1/_7\) | M1M1: — |
| \(= ^{225}_{448}\) or \(0.502\) (3 sfs) | A1: 3 |
In qns 2 & 3 "prod" means "product of two probabilities"
2(i) | $^4/_7$ or $0.571$ (3 sfs) | B1: 1 | |
2(ii) | $^1/_6 \times ^4/_7 + ^1/_6 \times ^3/_6$ | M1M1: — | M1: one correct prod or add any two prods; M1: all correct |
| $= ^{265}_{448}$ or $0.592$ (3 sfs) | A1: 3 | |
2(iii) | $^1/_6 \times ^3/_6 + ^5/_6 \times ^1/_7$ | M1M1: — | M1: one correct prod or add any two prods; M1: all correct |
| $= ^{225}_{448}$ or $0.502$ (3 sfs) | A1: 3 | |
**Total: 7**
---2 A bag contains 5 black discs and 3 red discs. A disc is selected at random from the bag. If it is red it is replaced in the bag. If it is black, it is not replaced. A second disc is now selected at random from the bag.
Find the probability that\\
(i) the second disc is black, given that the first disc was black,\\
(ii) the second disc is black,\\
(iii) the two discs are of different colours.
\hfill \mbox{\textit{OCR S1 2006 Q2 [7]}}