CAIE S1 2015 November — Question 2 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2015
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCombinations & Selection
TypeProbability of specific committee composition
DifficultyModerate -0.8 This is a straightforward application of combinations to calculate a single probability: C(9,6)/C(16,6). It requires only basic understanding of selection without replacement and no multi-step reasoning or problem-solving insight, making it easier than average but not trivial since students must correctly identify the sample space.
Spec5.01a Permutations and combinations: evaluate probabilities5.01b Selection/arrangement: probability problems
2 A committee of 6 people is to be chosen at random from 7 men and 9 women. Find the probability that there are no men on the committee.
Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(P(\text{no men}) = \frac{^9C_6}{^{16}C_6} = \frac{84}{8008} = \frac{21}{2002} = \frac{3}{286}\)B1 \(^9C_6\) seen anywhere
B1\(^{16}C_6\) seen as denom of fraction oe
\(= 0.0105\)B1 (3) Correct final answer
OR \(\frac{9}{16} \times \frac{8}{15} \times \frac{7}{14} \times \frac{6}{13} \times \frac{5}{12} \times \frac{4}{11} = 0.0105\)B1 \((9 \times 8 \times 7 \times 6 \times 5 \times 4)\) seen anywhere
B1Correct unsimplified denom
B1Correct final answer 
## Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(\text{no men}) = \frac{^9C_6}{^{16}C_6} = \frac{84}{8008} = \frac{21}{2002} = \frac{3}{286}$ | B1 | $^9C_6$ seen anywhere |
| | B1 | $^{16}C_6$ seen as denom of fraction oe |
| $= 0.0105$ | B1 (3) | Correct final answer |
| OR $\frac{9}{16} \times \frac{8}{15} \times \frac{7}{14} \times \frac{6}{13} \times \frac{5}{12} \times \frac{4}{11} = 0.0105$ | B1 | $(9 \times 8 \times 7 \times 6 \times 5 \times 4)$ seen anywhere |
| | B1 | Correct unsimplified denom |
| | B1 | Correct final answer |

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2 A committee of 6 people is to be chosen at random from 7 men and 9 women. Find the probability that there are no men on the committee.

\hfill \mbox{\textit{CAIE S1 2015 Q2 [3]}}
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