GATE 2015 EC – Question 59
The input $X$ 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 $Y = 0$, the conditional probability that '1' was transmitted is ________.
![A binary symmetric channel with $P[X = 0] = 0.2$ and $P[X = 1] = 0.8$. Each bit is received correctly with probability $\frac{6}{7}$ and flipped with probability $\frac{1}{7}$.](/question-images/GATE_EC_2015_Q59.png)
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Correct answer: 0.39 to 0.41
Explanation
By Bayes' rule, $P(X = 1 | Y = 0) = \frac{0.8 \times \frac{1}{7}}{0.8 \times \frac{1}{7} + 0.2 \times \frac{6}{7}} = \frac{0.8}{0.8 + 1.2} = 0.4$.