In a railway signalling system a signal is received by station A from the traffic control office and then transmitted to station B. At the origin the signal is yellow or red with probability and . Each station receives the signal correctly from its predecessor with probability . If the signal received at station B is yellow, the probability that the original signal was yellow is:
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In a railway signalling system a signal is received by station A from the traffic control office and then transmitted to station B. At the origin the signal is yellow or red with probability 4/5 and 1/5. Each station receives the signal correctly from its predecessor with probability 3/4. If the signal received at station B is yellow, the probability that the original signal was yellow is: (A) 22/23 (B) 11/20 (C) 20/23 (D) 9/20
Probability and Bayes' theorem has come up 190 times in 7 exams since 2004.
This question is on Total probability and Bayes' theorem, part of Probability and Bayes' theorem in Statistics.
Reversing a conditional probability and updating beliefs from evidence.
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Question from the DSE 2016 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.