| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tree Diagrams |
| Type | Conditional probability from tree |
| Difficulty | Moderate -0.3 This is a straightforward conditional probability question using a tree diagram with clearly stated percentages. The setup requires basic probability tree construction and applying Bayes' theorem formula, which are standard S1 techniques. The calculation is routine with no conceptual tricks, making it slightly easier than average. |
| Spec | 2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles |
3 It was found that $68 \%$ of the passengers on a train used a cell phone during their train journey. Of those using a cell phone, $70 \%$ were under 30 years old, $25 \%$ were between 30 and 65 years old and the rest were over 65 years old. Of those not using a cell phone, $26 \%$ were under 30 years old and $64 \%$ were over 65 years old.\\
(i) Draw a tree diagram to represent this information, giving all probabilities as decimals.\\
(ii) Given that one of the passengers is 45 years old, find the probability of this passenger using a cell phone during the journey.
\hfill \mbox{\textit{CAIE S1 2010 Q3 [5]}}