Moderate -0.8 This is a straightforward application of Bayes' theorem with clearly defined probabilities and a single calculation required. The problem setup is simple with only two locations and given probabilities, requiring students to identify P(A|B) = P(B|A)P(A)/P(B) and compute one fraction—easier than average A-level work.
2 When Ted is looking for his pen, the probability that it is in his pencil case is 0.7 . If his pen is in his pencil case he always finds it. If his pen is somewhere else, the probability that he finds it is 0.2 . Given that Ted finds his pen when he is looking for it, find the probability that it was in his pencil case.
2 When Ted is looking for his pen, the probability that it is in his pencil case is 0.7 . If his pen is in his pencil case he always finds it. If his pen is somewhere else, the probability that he finds it is 0.2 . Given that Ted finds his pen when he is looking for it, find the probability that it was in his pencil case.
\hfill \mbox{\textit{CAIE S1 2011 Q2 [4]}}