| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | September |
| Marks | 7 |
| Topic | Probability Definitions |
| Type | Sequential selection with conditional outcomes |
| Difficulty | Challenging +1.2 Part (i) is trivial probability reasoning (3/5). Part (ii) requires basic conditional probability (3/5 × 2/4). Part (iii) is substantially harder, requiring systematic enumeration of valid sequences where black count always exceeds white count—this demands careful case analysis and combinatorial thinking beyond routine exercises. The progression from routine to non-standard problem-solving elevates this above average difficulty. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
13 Bag A contains 3 black discs and 2 white discs only. Initially Bag B is empty. Discs are removed at random from bag A, and are placed in bag B, one at a time, until all 5 discs are in bag B.\\
(i) Write down the probability that the last disc that is placed in bag B is black.\\
(ii) Find the probability that the first disc and the last disc that are placed in bag B are both black.\\
(iii) Find the probability that, starting from when the first disc is placed in bag B , the number of black discs in bag B is always greater than the number of white discs in bag B.
\hfill \mbox{\textit{OCR H240/02 2018 Q13 [7]}}