| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2019 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Random selection fairness |
| Difficulty | Easy -1.2 This question tests understanding of the definition of random selection (equal probability) rather than computational skills. Part (i) requires recognizing that D has probability 1/2 while others have 1/6. Parts (ii) and (iii) involve straightforward application of this principle to design fair selection schemes. No calculations or problem-solving required—purely conceptual recall and basic reasoning. |
| Spec | 2.01a Population and sample: terminology2.01c Sampling techniques: simple random, opportunity, etc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(D\) more likely to be chosen | B1 | oe, e.g. \(P(D) > P(A)\), e.g. \(P(A)=P(B)=P(C)=\frac{1}{6}\), \(P(D)=\frac{1}{2}\); no contradictions |
| Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Reject scores of 5 or 6 | B1 | or other correct: choose \(D\) when the score is 4 |
| Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| AB AC AD BC BD CD | B1 | |
| Allocate as follows: 1: AB; 2: AC; 3: AD; 4: BC; 5: BD; 6: CD | B1 | or similar |
| Total: 2 |
**Question 3(i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $D$ more likely to be chosen | B1 | oe, e.g. $P(D) > P(A)$, e.g. $P(A)=P(B)=P(C)=\frac{1}{6}$, $P(D)=\frac{1}{2}$; no contradictions |
| **Total: 1** | | |
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**Question 3(ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| Reject scores of 5 or 6 | B1 | or other correct: choose $D$ when the score is 4 |
| **Total: 1** | | |
## Question 3(iii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| AB AC AD BC BD CD | B1 | |
| Allocate as follows: 1: AB; 2: AC; 3: AD; 4: BC; 5: BD; 6: CD | B1 | or similar |
| **Total: 2** | | |
---3 Luis has to choose one person at random from four people, $A , B , C$ and $D$. He throws a fair six-sided die. If the score is 1 , he will choose $A$. If the score is 2 he will choose $B$. If the score is 3 , he will choose $C$. If the score is 4 or more he will choose $D$.\\
(i) Explain why the choice made by this method is not random.\\
(ii) Describe how Luis could use a single throw of the die to make a random choice.\\
On another day, Luis has to choose two people at random from the same four people, $A , B , C$ and $D$.\\
(iii) List the possible choices of two people and hence describe how Luis could use a single throw of the die to make this random choice.\\
\hfill \mbox{\textit{CAIE S2 2019 Q3 [4]}}