CAIE S1 2017 June — Question 1 4 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2017
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicProbability Definitions
TypeDice probability problems
DifficultyModerate -0.3 This is a straightforward probability question requiring students to list favorable outcomes for a sum of 9 (pairs: 3+6, 4+5, 5+4, 6+3), calculate each probability using given values, and sum them. It's slightly easier than average as it involves basic enumeration and multiplication of probabilities with no conceptual subtlety, though the biased die adds minor complexity over a standard fair die problem.
Spec2.03a Mutually exclusive and independent events

1 A biased die has faces numbered 1 to 6 . The probabilities of the die landing on 1,3 or 5 are each equal to 0.1 . The probabilities of the die landing on 2 or 4 are each equal to 0.2 . The die is thrown twice. Find the probability that the sum of the numbers it lands on is 9 .

Question 1:
AnswerMarks Guidance
AnswerMark Guidance
\(P(6) = 0.3\)B1 SOI
\(P(\text{sum is } 9) = P(3,6) + P(4,5) + P(5,4) + P(6,3)\)M1 Identifying the four ways of summing to 9: \((3,6)\), \((6,3)\), \((4,5)\) and \((5,4)\)
\(= (0.03 + 0.02) \times 2\)M1 Mult 2 probs together to find one correct prob of \((3,6)\), \((6,3)\), \((4,5)\) or \((5,4)\) unsimplified
\(= 0.1\)A1 OE
Total: 4
# Question 1:

| Answer | Mark | Guidance |
|--------|------|----------|
| $P(6) = 0.3$ | B1 | SOI |
| $P(\text{sum is } 9) = P(3,6) + P(4,5) + P(5,4) + P(6,3)$ | M1 | Identifying the four ways of summing to 9: $(3,6)$, $(6,3)$, $(4,5)$ and $(5,4)$ |
| $= (0.03 + 0.02) \times 2$ | M1 | Mult 2 probs together to find one correct prob of $(3,6)$, $(6,3)$, $(4,5)$ or $(5,4)$ unsimplified |
| $= 0.1$ | A1 | OE |
| **Total: 4** | | |
1 A biased die has faces numbered 1 to 6 . The probabilities of the die landing on 1,3 or 5 are each equal to 0.1 . The probabilities of the die landing on 2 or 4 are each equal to 0.2 . The die is thrown twice. Find the probability that the sum of the numbers it lands on is 9 .\\

\hfill \mbox{\textit{CAIE S1 2017 Q1 [4]}}