CAIE S1 2017 November — Question 1 2 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2017
SessionNovember
Marks2
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndependent Events
TypeIndependent repeated trials
DifficultyEasy -1.2 This is a straightforward application of complement rule with independent trials requiring only P(at least one) = 1 - P(none) = 1 - 0.8³. It's a standard textbook exercise with minimal steps and no conceptual challenge beyond basic probability rules.
Spec2.03a Mutually exclusive and independent events
1 A statistics student asks people to complete a survey. The probability that a randomly chosen person agrees to complete the survey is 0.2 . Find the probability that at least one of the first three people asked agrees to complete the survey.
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
EITHER: \(P(\text{at least 1 completes}) = 1 - P(\text{0 people complete}) = 1 - (0.8)^3\)M1 Fully correct unsimplified expression \(1-(0.8)^3\) OE
\(= 0.488 \left(\frac{61}{125}\right)\)A1
OR1: \(P(1,2,3) = {}^3C_1(0.2)(0.8)^2 + {}^3C_2(0.2)^2(0.8) + (0.2)^3\)M1 Unsimplified correct 3 term expression
\(= 0.488 \left(\frac{61}{125}\right)\)A1
OR2: \(0.2 + 0.8\times0.2 + 0.8\times0.8\times0.2\)M1 Unsimplified sum of 3 correct terms
\(= 0.488 \left(\frac{61}{125}\right)\)A1
Total: 2 
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| **EITHER:** $P(\text{at least 1 completes}) = 1 - P(\text{0 people complete}) = 1 - (0.8)^3$ | M1 | Fully correct unsimplified expression $1-(0.8)^3$ OE |
| $= 0.488 \left(\frac{61}{125}\right)$ | A1 | |
| **OR1:** $P(1,2,3) = {}^3C_1(0.2)(0.8)^2 + {}^3C_2(0.2)^2(0.8) + (0.2)^3$ | M1 | Unsimplified correct 3 term expression |
| $= 0.488 \left(\frac{61}{125}\right)$ | A1 | |
| **OR2:** $0.2 + 0.8\times0.2 + 0.8\times0.8\times0.2$ | M1 | Unsimplified sum of 3 correct terms |
| $= 0.488 \left(\frac{61}{125}\right)$ | A1 | |
| **Total: 2** | | |

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1 A statistics student asks people to complete a survey. The probability that a randomly chosen person agrees to complete the survey is 0.2 . Find the probability that at least one of the first three people asked agrees to complete the survey.\\

\hfill \mbox{\textit{CAIE S1 2017 Q1 [2]}}
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