CAIE S1 2016 March — Question 2 4 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2016
SessionMarch
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDiscrete Probability Distributions
TypeConstruct probability distribution from scenario
DifficultyModerate -0.8 This is a straightforward probability distribution question requiring systematic enumeration of cases (0, 1, or 2 white roses) using combinations. The calculations are routine: P(X=0) = C(8,3)/C(10,3), P(X=1) = C(2,1)×C(8,2)/C(10,3), P(X=2) = C(2,2)×C(8,1)/C(10,3). It tests basic understanding of combinations and probability distributions but requires no problem-solving insight, making it easier than average.
Spec2.04a Discrete probability distributions
2 A flower shop has 5 yellow roses, 3 red roses and 2 white roses. Martin chooses 3 roses at random. Draw up the probability distribution table for the number of white roses Martin chooses.
Question 2:
AnswerMarks Guidance
No of W0 1
Prob42/90 42/90
\(P(0) = \frac{8}{10} \times \frac{7}{9} \times \frac{6}{8} = \frac{42}{90}\)B1 0, 1, 2 seen in table with attempt at prob.
\(P(1W) = P(\text{W,NW, NW}) \times 3 = \frac{2}{10} \times \frac{8}{9} \times \frac{7}{8} \times 3 = \frac{42}{90}\)M1, M1 3-factor prob seen with different denoms.; mult by 3
\(P(2W) = P(\text{W, W, NW}) \times 3 = \frac{2}{10} \times \frac{1}{9} \times \frac{8}{8} \times 3 = \frac{6}{90}\)A1 (4) All correct 
## Question 2:

| No of W | 0 | 1 | 2 |
|---------|-------|-------|------|
| Prob | 42/90 | 42/90 | 6/90 |

$P(0) = \frac{8}{10} \times \frac{7}{9} \times \frac{6}{8} = \frac{42}{90}$ | B1 | 0, 1, 2 seen in table with attempt at prob.

$P(1W) = P(\text{W,NW, NW}) \times 3 = \frac{2}{10} \times \frac{8}{9} \times \frac{7}{8} \times 3 = \frac{42}{90}$ | M1, M1 | 3-factor prob seen with different denoms.; mult by 3

$P(2W) = P(\text{W, W, NW}) \times 3 = \frac{2}{10} \times \frac{1}{9} \times \frac{8}{8} \times 3 = \frac{6}{90}$ | A1 (4) | All correct

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2 A flower shop has 5 yellow roses, 3 red roses and 2 white roses. Martin chooses 3 roses at random. Draw up the probability distribution table for the number of white roses Martin chooses.

\hfill \mbox{\textit{CAIE S1 2016 Q2 [4]}}
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