CAIE S1 2009 November — Question 3 6 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2009
SessionNovember
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConditional Probability
TypeBayes with complementary outcome
DifficultyModerate -0.8 This is a straightforward application of Bayes' theorem using a tree diagram with simple probabilities. The question requires basic probability rules (multiplication and addition along branches) and one conditional probability calculation, but involves no conceptual difficulty beyond standard S1 material and requires only routine algebraic manipulation.
Spec2.03b Probability diagrams: tree, Venn, sample space2.03c Conditional probability: using diagrams/tables2.03d Calculate conditional probability: from first principles

3 Maria chooses toast for her breakfast with probability 0.85 . If she does not choose toast then she has a bread roll. If she chooses toast then the probability that she will have jam on it is 0.8 . If she has a bread roll then the probability that she will have jam on it is 0.4 .
  1. Draw a fully labelled tree diagram to show this information.
  2. Given that Maria did not have jam for breakfast, find the probability that she had toast.

3 Maria chooses toast for her breakfast with probability 0.85 . If she does not choose toast then she has a bread roll. If she chooses toast then the probability that she will have jam on it is 0.8 . If she has a bread roll then the probability that she will have jam on it is 0.4 .\\
(i) Draw a fully labelled tree diagram to show this information.\\
(ii) Given that Maria did not have jam for breakfast, find the probability that she had toast.

\hfill \mbox{\textit{CAIE S1 2009 Q3 [6]}}