CAIE S1 2012 November — Question 1 4 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2012
SessionNovember
Marks4
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Mark schemeDownload PDF ↗
TopicDiscrete Probability Distributions
TypeConstruct probability distribution from scenario
DifficultyModerate -0.8 This is a straightforward application of combinations to construct a probability distribution. Students need to calculate P(X=0), P(X=1), P(X=2), P(X=3) using C(3,r)×C(7,3-r)/C(10,3), which is a standard textbook exercise requiring only routine application of the hypergeometric distribution formula with small numbers and no additional problem-solving or interpretation.
Spec5.02a Discrete probability distributions: general5.02b Expectation and variance: discrete random variables
1 Ashok has 3 green pens and 7 red pens. His friend Rod takes 3 of these pens at random, without replacement. Draw up a probability distribution table for the number of green pens Rod takes.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(P(0) = \frac{7}{10} \times \frac{6}{9} \times \frac{5}{8} = \frac{210}{720}\)B1 Finding P(0, 1, 2, 3); 1 or 2 correct
\(P(1) = \frac{3}{10} \times \frac{7}{9} \times \frac{6}{8} \times 3C1 = \frac{378}{720}\)B1 3 correct
\(P(2) = \frac{3}{10} \times \frac{2}{9} \times \frac{7}{8} \times 3C2 = \frac{126}{720}\)B1
\(P(3) = \frac{3}{10} \times \frac{2}{9} \times \frac{1}{8} = \frac{6}{720}\ (\frac{1}{120})\)B1 [4] All correct 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(0) = \frac{7}{10} \times \frac{6}{9} \times \frac{5}{8} = \frac{210}{720}$ | B1 | Finding P(0, 1, 2, 3); 1 or 2 correct |
| $P(1) = \frac{3}{10} \times \frac{7}{9} \times \frac{6}{8} \times 3C1 = \frac{378}{720}$ | B1 | 3 correct |
| $P(2) = \frac{3}{10} \times \frac{2}{9} \times \frac{7}{8} \times 3C2 = \frac{126}{720}$ | B1 | |
| $P(3) = \frac{3}{10} \times \frac{2}{9} \times \frac{1}{8} = \frac{6}{720}\ (\frac{1}{120})$ | B1 [4] | All correct |

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1 Ashok has 3 green pens and 7 red pens. His friend Rod takes 3 of these pens at random, without replacement. Draw up a probability distribution table for the number of green pens Rod takes.

\hfill \mbox{\textit{CAIE S1 2012 Q1 [4]}}
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Q1 4 Q2 5 Q3 6 Q4 7 Q5 7 Q6 9 Q7 12