| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tree Diagrams |
| Type | Find unknown probability parameter |
| Difficulty | Moderate -0.8 This is a straightforward tree diagram problem requiring basic probability rules: part (i) uses the law of total probability (0.2×0.75 + 0.8×x = 0.5) to find x, and part (ii) applies Bayes' theorem with values already computed. Both are standard textbook exercises with clear methods and minimal steps. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(0.8\) seen | B1 | |
| \(0.8x + (0.2)\times(0.75) = 0.5\) | M1 | Summing two 2-term brackets |
| M1 | Equating their LHS containing \(x\) to \(0.5\) | |
| \(x = 0.438\) | A1 | 4 Correct answer |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(P(S \text{ given } B) = 0.15/0.5\) | M1 | Correct numerator |
| \(= 0.3\) | A1 | 2 Correct answer |
## Question 2(i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $0.8$ seen | B1 | |
| $0.8x + (0.2)\times(0.75) = 0.5$ | M1 | Summing two 2-term brackets |
| | M1 | Equating their LHS containing $x$ to $0.5$ |
| $x = 0.438$ | A1 | **4** Correct answer |
## Question 2(ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(S \text{ given } B) = 0.15/0.5$ | M1 | Correct numerator |
| $= 0.3$ | A1 | **2** Correct answer |
---2 The probability that Henk goes swimming on any day is 0.2 . On a day when he goes swimming, the probability that Henk has burgers for supper is 0.75 . On a day when he does not go swimming the probability that he has burgers for supper is $x$. This information is shown on the following tree diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{14e8a601-2180-4491-9336-cafd262f2596-2_693_1038_845_555}
The probability that Henk has burgers for supper on any day is 0.5 .\\
(i) Find $x$.\\
(ii) Given that Henk has burgers for supper, find the probability that he went swimming that day.
\hfill \mbox{\textit{CAIE S1 2006 Q2 [6]}}