CAIE S1 2015 November — Question 1 4 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2015
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Distribution
TypeDirect binomial probability calculation
DifficultyModerate -0.8 This is a straightforward binomial probability calculation requiring only the complement rule (P(X < 10) = 1 - P(X ≥ 10)) and calculator use. The setup is direct with clearly stated parameters (n=11, p=0.76), requiring no problem-solving insight—just routine application of the binomial formula or tables.
Spec2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities
1 In a certain town, 76\% of cars are fitted with satellite navigation equipment. A random sample of 11 cars from this town is chosen. Find the probability that fewer than 10 of these cars are fitted with this equipment.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(p = 0.76\)
\(P(\text{fewer than } 10) = 1 - P(10, 11)\)M1 Any binomial term \(^{11}C_x p^x (1-p)^{11-x}\), \(0 < p < 1\)
\(= 1 - (0.76)^{10}(0.24)^1 \cdot {}^{11}C_{10} - (0.76)^{11}\)M1 Any binomial term \(^nC_x(0.76)^x(0.24)^{n-x}\)
\(= 1 - 0.219\)M1 \(1 - P(10, 11)\) oe binomial expression
\(= 0.781\)A1 [4] Correct answer 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $p = 0.76$ | | |
| $P(\text{fewer than } 10) = 1 - P(10, 11)$ | M1 | Any binomial term $^{11}C_x p^x (1-p)^{11-x}$, $0 < p < 1$ |
| $= 1 - (0.76)^{10}(0.24)^1 \cdot {}^{11}C_{10} - (0.76)^{11}$ | M1 | Any binomial term $^nC_x(0.76)^x(0.24)^{n-x}$ |
| $= 1 - 0.219$ | M1 | $1 - P(10, 11)$ oe binomial expression |
| $= 0.781$ | A1 [4] | Correct answer |

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1 In a certain town, 76\% of cars are fitted with satellite navigation equipment. A random sample of 11 cars from this town is chosen. Find the probability that fewer than 10 of these cars are fitted with this equipment.

\hfill \mbox{\textit{CAIE S1 2015 Q1 [4]}}
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Q1 4 Q2 4 Q3 6 Q4 7 Q5 9 Q6 9 Q7 11