| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Standard Bayes with discrete events |
| Difficulty | Moderate -0.8 This is a straightforward two-part Bayes' theorem question with simple probabilities (0.5, 1.0, 0.6) and clear structure. Part (i) requires basic tree diagram/law of total probability, part (ii) is direct application of Bayes' formula. No conceptual difficulty beyond standard S1 material, and the numbers are designed to be easy to work with. |
| 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 | Mark | Guidance |
| \(P(\text{team}) = 0.5 + 0.5 \times 0.6\) | B1 | One correct product |
| M1 | Summing two 2-factor products | |
| \(= 0.8\) | A1 3 | Correct answer |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(P(\text{training session} \mid \text{team}) = \dfrac{0.5}{0.5 + 0.5 \times 0.6}\) | M1 | Selecting correct term from (i) as their numerator |
| M1 | Dividing by their (i) (must be \(< 1\)) | |
| \(= 0.625\) \((5/8)\) | A1 3 | Correct answer |
## Question 2:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $P(\text{team}) = 0.5 + 0.5 \times 0.6$ | B1 | One correct product |
| | M1 | Summing two 2-factor products |
| $= 0.8$ | A1 **3** | Correct answer |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $P(\text{training session} \mid \text{team}) = \dfrac{0.5}{0.5 + 0.5 \times 0.6}$ | M1 | Selecting correct term from (i) as their numerator |
| | M1 | Dividing by their (i) (must be $< 1$) |
| $= 0.625$ $(5/8)$ | A1 **3** | Correct answer |
---2 Jamie is equally likely to attend or not to attend a training session before a football match. If he attends, he is certain to be chosen for the team which plays in the match. If he does not attend, there is a probability of 0.6 that he is chosen for the team.\\
(i) Find the probability that Jamie is chosen for the team.\\
(ii) Find the conditional probability that Jamie attended the training session, given that he was chosen for the team.
\hfill \mbox{\textit{CAIE S1 2007 Q2 [6]}}