CAIE S1 2017 March — Question 2 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2017
SessionMarch
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicHypergeometric Distribution
TypeCalculate single probability value
DifficultyModerate -0.5 This is a straightforward application of the hypergeometric distribution formula with clearly stated parameters (40 total, 12 green, 7 selected, want exactly 3 green). It requires only direct substitution into the formula and calculator computation, making it slightly easier than average but not trivial due to the computational complexity of the combinations involved.
Spec5.01a Permutations and combinations: evaluate probabilities
2 A bag contains 10 pink balloons, 9 yellow balloons, 12 green balloons and 9 white balloons. 7 balloons are selected at random without replacement. Find the probability that exactly 3 of them are green.
Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
\(\dfrac{^{12}C_3 \times\, ^{28}C_4}{^{40}C_7}\)M1 Using combinations with attempt to evaluate 2 terms in num. and 1 in denom.
M1Correct numerator or denominator unsimplified
\(= 0.242\)A1
OR
\(P(GGG) = \dfrac{12}{40}\times\dfrac{11}{39}\times\dfrac{10}{38}\times\dfrac{28}{37}\times\dfrac{27}{36}\times\dfrac{26}{35}\times\dfrac{25}{34}\times\,^7C_3\)M1 Multiplying 3 green probs with 4 non-green probs, without replacement
M1Multiplying by \(^7C_3\)
\(= 0.242\)A1 
# Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\dfrac{^{12}C_3 \times\, ^{28}C_4}{^{40}C_7}$ | M1 | Using combinations with attempt to evaluate 2 terms in num. and 1 in denom. |
| | M1 | Correct numerator or denominator unsimplified |
| $= 0.242$ | A1 | |
| **OR** | | |
| $P(GGG) = \dfrac{12}{40}\times\dfrac{11}{39}\times\dfrac{10}{38}\times\dfrac{28}{37}\times\dfrac{27}{36}\times\dfrac{26}{35}\times\dfrac{25}{34}\times\,^7C_3$ | M1 | Multiplying 3 green probs with 4 non-green probs, without replacement |
| | M1 | Multiplying by $^7C_3$ |
| $= 0.242$ | A1 | |

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2 A bag contains 10 pink balloons, 9 yellow balloons, 12 green balloons and 9 white balloons. 7 balloons are selected at random without replacement. Find the probability that exactly 3 of them are green.\\

\hfill \mbox{\textit{CAIE S1 2017 Q2 [3]}}
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