CAIE S1 2006 November — Question 4 7 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2006
SessionNovember
Marks7
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Mark schemeDownload PDF ↗
TopicProbability Definitions
TypeMutually exclusive events
DifficultyModerate -0.8 This is a straightforward probability question requiring systematic enumeration of outcomes from two dice. Parts (i) and (ii) involve counting favorable outcomes from 36 equally likely cases using basic arithmetic conditions, while part (iii) tests understanding of the definition of mutually exclusive events. All techniques are standard S1 material with no problem-solving insight required beyond careful counting.
Spec2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space
4 Two fair dice are thrown.
  1. Event \(A\) is 'the scores differ by 3 or more'. Find the probability of event \(A\).
  2. Event \(B\) is 'the product of the scores is greater than 8 '. Find the probability of event \(B\).
  3. State with a reason whether events \(A\) and \(B\) are mutually exclusive.
(i) List: \(14, 15, 16, 25, 26, 36\) and reversed
\(P(\text{scores differ by } 3 \text{ or more}) = \frac{12}{36} = \frac{1}{3}(0.333)\)
AnswerMarks Guidance
M1For an attempt at listing
A1, A13 marks Selecting at least 6 correct pairs. Correct answer
(ii) \(\frac{20}{36}\)
AnswerMarks Guidance
M1Some identification on the list, must include one of \(25, 26, 33, 34, 35\)
A12 marks Correct answer
(iii) \(P(A \cap B) \neq 0\) implies not mut excl, or equivalent
\(P(A \cap B) = \frac{6}{36}\) so not mut excl
AnswerMarks Guidance
B1Correct statement about mut excl events
B1 ft2 marks Correct answer using their data 
**(i)** List: $14, 15, 16, 25, 26, 36$ and reversed

$P(\text{scores differ by } 3 \text{ or more}) = \frac{12}{36} = \frac{1}{3}(0.333)$

| M1 | For an attempt at listing |
| A1, A1 | 3 marks | Selecting at least 6 correct pairs. Correct answer |

**(ii)** $\frac{20}{36}$

| M1 | Some identification on the list, must include one of $25, 26, 33, 34, 35$ |
| A1 | 2 marks | Correct answer |

**(iii)** $P(A \cap B) \neq 0$ implies not mut excl, or equivalent

$P(A \cap B) = \frac{6}{36}$ so not mut excl

| B1 | Correct statement about mut excl events |
| B1 ft | 2 marks | Correct answer using their data |

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4 Two fair dice are thrown.\\
(i) Event $A$ is 'the scores differ by 3 or more'. Find the probability of event $A$.\\
(ii) Event $B$ is 'the product of the scores is greater than 8 '. Find the probability of event $B$.\\
(iii) State with a reason whether events $A$ and $B$ are mutually exclusive.

\hfill \mbox{\textit{CAIE S1 2006 Q4 [7]}}
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