CAIE S1 2019 November — Question 1 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2019
SessionNovember
Marks3
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TopicConditional Probability
TypeFinding unknown probability from total probability
DifficultyModerate -0.8 This is a straightforward application of the law of total probability with one unknown. Students need to set up P(not late) = P(bus)×P(not late|bus) + P(cycle)×P(not late|cycle) = 0.8×0.6 + 0.2×(1-x) = 0.63, then solve the linear equation. It requires only basic probability tree manipulation and simple algebra, making it easier than average.
Spec2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables
1 When Shona goes to college she either catches the bus with probability 0.8 or she cycles with probability 0.2 . If she catches the bus, the probability that she is late is 0.4 . If she cycles, the probability that she is late is \(x\). The probability that Shona is not late for college on a randomly chosen day is 0.63 . Find the value of \(x\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(0.8 \times 0.6 + 0.2(1-x) = 0.63\)M1 Equation of form \(0.8 \times A + 0.2 \times B = C\), A,B involving \(1-x\) and 0.6 or 0.4 and \(C = 0.63\) or 0.37
\(0.2x = 0.05\)M1 Correct unsimplified equation
\(x = 0.25\)A1
Alternative method:
AnswerMarks Guidance
AnswerMarks Guidance
\(0.8 \times 0.4 + 0.2x = 1 - 0.63\)M1 Equation of form \(0.8 \times A + 0.2 \times B = C\), A,B involving \(x\) and 0.6 or 0.4 and \(C = 0.63\) or 0.37
\(0.2x = 0.05\)M1 Correct unsimplified equation
\(x = 0.25\)A1
Total: 3 marks
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.8 \times 0.6 + 0.2(1-x) = 0.63$ | M1 | Equation of form $0.8 \times A + 0.2 \times B = C$, A,B involving $1-x$ and 0.6 or 0.4 and $C = 0.63$ or 0.37 |
| $0.2x = 0.05$ | M1 | Correct unsimplified equation |
| $x = 0.25$ | A1 | |

**Alternative method:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.8 \times 0.4 + 0.2x = 1 - 0.63$ | M1 | Equation of form $0.8 \times A + 0.2 \times B = C$, A,B involving $x$ and 0.6 or 0.4 and $C = 0.63$ or 0.37 |
| $0.2x = 0.05$ | M1 | Correct unsimplified equation |
| $x = 0.25$ | A1 | |

**Total: 3 marks**

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1 When Shona goes to college she either catches the bus with probability 0.8 or she cycles with probability 0.2 . If she catches the bus, the probability that she is late is 0.4 . If she cycles, the probability that she is late is $x$. The probability that Shona is not late for college on a randomly chosen day is 0.63 . Find the value of $x$.\\

\hfill \mbox{\textit{CAIE S1 2019 Q1 [3]}}
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