GATE 2014 EC (EC4) – Question 60
The Z-channel shown has equiprobable inputs 0,1. Given that output is 0, find the probability input was 0.
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Show answer and explanation
Correct answer: 0.79 to 0.81
Explanation
The joint probability of input0and output0is(1/2)×1=1/2. Total output0probability is(1/2)×1+(1/2)×0.25=5/8. Bayes’ rule therefore gives(1/2)/(5/8)=**4/5=0.8**. Equal input priors do not make the posterior equal after observing a channel output.