| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2002 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Probability Definitions |
| Type | Listing outcomes and counting |
| Difficulty | Easy -1.2 This is a straightforward counting problem requiring systematic listing of outcomes and basic probability calculation. The question explicitly guides students to list outcomes for part (i), and part (ii) is a direct repetition of the same method. No complex reasoning or problem-solving insight is needed—just careful enumeration and division by 216. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Answer | Marks | Guidance |
|---|---|---|
| Part (i): Options (122), (212), (221), (113), (131), (311) | M1 | For an option involving (1,2,2) and an option involving (1,1,3) |
| A1 | For all six correct options | |
| A1 | 3 | For legitimately obtaining answer given |
| \(\text{prob} = 6/216 \text{ (AG)}\) | ||
| Part (ii): (133) × 3, (223) × 3, (115) × 3, (124) × 6 | M1 | For listing 3 or 4 different correct options or tree diagram |
| M1 ind | For multiplying 4 prob options by a relevant number or listing \(\geq 12\) correct options | |
| A1 | 3 | For correct answer |
| \(\text{prob} = 15/216 \text{ (= 5/72)}\) |
**Part (i):** Options (122), (212), (221), (113), (131), (311) | M1 | For an option involving (1,2,2) and an option involving (1,1,3)
| A1 | For all six correct options
| A1 | 3 | For legitimately obtaining answer given
$\text{prob} = 6/216 \text{ (AG)}$ | |
**Part (ii):** (133) × 3, (223) × 3, (115) × 3, (124) × 6 | M1 | For listing 3 or 4 different correct options or tree diagram
| M1 ind | For multiplying 4 prob options by a relevant number or listing $\geq 12$ correct options
| A1 | 3 | For correct answer
$\text{prob} = 15/216 \text{ (= 5/72)}$ | |
---2 Ivan throws three fair dice.\\
(i) List all the possible scores on the three dice which give a total score of 5 , and hence show that the probability of Ivan obtaining a total score of 5 is $\frac { 1 } { 36 }$.\\
(ii) Find the probability of Ivan obtaining a total score of 7.
\hfill \mbox{\textit{CAIE S1 2002 Q2 [6]}}