CAIE S1 2021 June — Question 1 4 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2021
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCombinations & Selection
TypeCommittee with gender/category constraints
DifficultyModerate -0.3 This is a straightforward combinations problem requiring students to identify two cases (4 red + 1 blue, or 5 red, or 4 blue + 1 red) and apply the basic formula C(n,r). The 'at least' condition is simple to handle with only two scenarios, making this slightly easier than average but still requiring proper case analysis.
Spec5.01b Selection/arrangement: probability problems
1 A bag contains 12 marbles, each of a different size. 8 of the marbles are red and 4 of the marbles are blue. How many different selections of 5 marbles contain at least 4 marbles of the same colour?
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
RRRRB: \(^8C_4 \times ^4C_1 = 280\)M1 \(^8C_x \times ^4C_y\) with \(x + y = 5\), \(x, y\) both integers, \(1 \leqslant x \leqslant 5\), \(0 \leqslant y \leqslant 4\); condone \(^8C_1 \times 1\)
BBBBR: \(^8C_1 \times ^4C_4 = 8\)A1 Two correct outcomes evaluated
RRRRR: \(^8C_5 = 56\)M1 Add 2 or 3 identified correct scenarios only (no additional terms, not probabilities)
[Total =] 344A1 WWW, only dependent on 2nd M mark
4SC not all (or no) scenarios identified: B1 \(280 + 8 + 56\) DB1 \(344\) 
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| RRRRB: $^8C_4 \times ^4C_1 = 280$ | M1 | $^8C_x \times ^4C_y$ with $x + y = 5$, $x, y$ both integers, $1 \leqslant x \leqslant 5$, $0 \leqslant y \leqslant 4$; condone $^8C_1 \times 1$ |
| BBBBR: $^8C_1 \times ^4C_4 = 8$ | A1 | Two correct outcomes evaluated |
| RRRRR: $^8C_5 = 56$ | M1 | Add 2 or 3 identified correct scenarios only (no additional terms, not probabilities) |
| [Total =] 344 | A1 | WWW, only dependent on 2nd M mark |
| | **4** | SC not all (or no) scenarios identified: **B1** $280 + 8 + 56$ **DB1** $344$ |

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1 A bag contains 12 marbles, each of a different size. 8 of the marbles are red and 4 of the marbles are blue.

How many different selections of 5 marbles contain at least 4 marbles of the same colour?\\

\hfill \mbox{\textit{CAIE S1 2021 Q1 [4]}}
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