GATE EC 2015 Set 1 — Question 59
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Communications → Information Theory → Bayes' Theorem
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Question
The input to the Binary Symmetric Channel (BSC) shown in the figure is '1' with probability 0.8. The cross-over probability is 1/7. If the received bit , the conditional probability that '1' was transmitted is ________.
Correct answer
0.39 to 0.41
Solution
Given:
Cross-over probability
From the BSC diagram:
We need to find . Using Bayes' Theorem:
First, calculate the total probability :
Now, substitute back into the Bayes' formula:
The conditional probability is 0.4.
Cross-over probability
From the BSC diagram:
We need to find . Using Bayes' Theorem:
First, calculate the total probability :
Now, substitute back into the Bayes' formula:
The conditional probability is 0.4.
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