| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2013 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Random selection fairness |
| Difficulty | Easy -1.8 This is a straightforward probability question requiring only basic understanding that fair selection means equal probabilities (1/3 each). Part (i) involves simple calculation that P(TT)=P(HH)=1/4 but P(one of each)=1/2, showing inequality. Part (ii) requires minimal creativity to suggest ignoring one outcome and repeating. No complex calculations or novel problem-solving needed. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| One of each is more likely; \(P(\text{one of each}) = 0.5\), \(P(HH) = 0.25\) | B1, B1 [2] | or \(P(TT) = 0.25\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Choose Charlie only if H then T; Throw again if T then H | B1, B1 [2] | or similar e.g. HH for A, HT for B, TT for C or vice versa |
## Question 1:
### Part (i):
| Answer | Mark | Guidance |
|--------|------|----------|
| One of each is more likely; $P(\text{one of each}) = 0.5$, $P(HH) = 0.25$ | B1, B1 [2] | or $P(TT) = 0.25$ |
### Part (ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| Choose Charlie only if H then T; Throw again if T then H | B1, B1 [2] | or similar e.g. HH for A, HT for B, TT for C or vice versa |
---1 Marie wants to choose one student at random from Anthea, Bill and Charlie. She throws two fair coins. If both coins show tails she will choose Anthea. If both coins show heads she will choose Bill. If the coins show one of each she will choose Charlie.\\
(i) Explain why this is not a fair method for choosing the student.\\
(ii) Describe how Marie could use the two coins to give a fair method for choosing the student.
\hfill \mbox{\textit{CAIE S2 2013 Q1 [4]}}