| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2008 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Combinations & Selection |
| Type | Critique of sampling methods |
| Difficulty | Easy -1.2 This is a straightforward conceptual question about sampling methods requiring students to recognize that sums of two dice don't produce uniform probabilities (e.g., 7 is most likely, 2 and 12 are least likely). No calculations needed, just basic understanding of probability distributions and random sampling. Easier than average A-level work. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Not all totals have the same probability e.g. P(7) = 6/36, P(4) = 3/36 | B1 [2] | Or equivalent. Any example to correctly justify their statement above |
| (ii) Any valid method e.g. using pieces of paper, calculator, random number tables | B1 | Valid idea |
| B1 [2] | Method of choosing – full description |
(i) Not all totals have the same probability e.g. P(7) = 6/36, P(4) = 3/36 | B1 [2] | Or equivalent. Any example to correctly justify their statement above
(ii) Any valid method e.g. using pieces of paper, calculator, random number tables | B1 | Valid idea
| B1 [2] | Method of choosing – full description
---1 Alan wishes to choose one child at random from the eleven children in his music class. The children are numbered $2,3,4$, and so on, up to 12 . Alan then throws two fair dice, each numbered from 1 to 6 , and chooses the child whose number is the sum of the scores on the two dice.\\
(i) Explain why this is an unsatisfactory method of choosing a child.\\
(ii) Describe briefly a satisfactory method of choosing a child.
\hfill \mbox{\textit{CAIE S2 2008 Q1 [4]}}