CAIE S1 2010 June — Question 1 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2010
SessionJune
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 defined parameters (52 total, 13 red, selecting 7, wanting exactly 3 red). It requires direct substitution into the formula with no conceptual complications or multi-step reasoning, making it slightly easier than average.
Spec5.01a Permutations and combinations: evaluate probabilities
1 A bottle of sweets contains 13 red sweets, 13 blue sweets, 13 green sweets and 13 yellow sweets. 7 sweets are selected at random. Find the probability that exactly 3 of them are red.
AnswerMarks Guidance
\(\frac{^{13}C_x \cdot ^{39}C_4}{^{52}C_7} = 0.176\)M1 Using combinations with attempt to evaluate product of 2 in num and only 1 in denom
M1Correct numerator or denominator
A1Correct answer
OR \(P(RRR) = \frac{13}{52} \times \frac{12}{51} \times \frac{11}{50} \times \frac{39}{49} \times \frac{38}{48} \times \frac{37}{47} \times \frac{36}{46} \times ^7C_3 = 0.176\)M1 OR Multiplying 3 unequal red probs with 4 unequal non-red probs
M1Multiplying a probability by \(^7C_3\)
A1Correct answer 
$\frac{^{13}C_x \cdot ^{39}C_4}{^{52}C_7} = 0.176$ | M1 | Using combinations with attempt to evaluate product of 2 in num and only 1 in denom |
| M1 | Correct numerator or denominator |
| A1 | Correct answer |

OR $P(RRR) = \frac{13}{52} \times \frac{12}{51} \times \frac{11}{50} \times \frac{39}{49} \times \frac{38}{48} \times \frac{37}{47} \times \frac{36}{46} \times ^7C_3 = 0.176$ | M1 | OR Multiplying 3 unequal red probs with 4 unequal non-red probs |
| M1 | Multiplying a probability by $^7C_3$ |
| A1 | Correct answer |

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1 A bottle of sweets contains 13 red sweets, 13 blue sweets, 13 green sweets and 13 yellow sweets. 7 sweets are selected at random. Find the probability that exactly 3 of them are red.

\hfill \mbox{\textit{CAIE S1 2010 Q1 [3]}}
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