A sender (S) transmits a signal, which can be one of the two kinds: H and L with probabilities 0.1 and 0.9 respectively, to a receiver (R). In the graph below, the weight of edge (u, v) is the probability of receiving v when u is transmitted, where u, v ∈ \H, L\. For example, the probability that the received signal is L given the transmitted signal was H, is 0.7. If the received signal is H, the probability that the transmitted signal was H (rounded to 2 decimal places) is ________.

GATE CSE 2021 Set 1 Q64: Bayes' rule on a noisy two-signal channel

Engineering Mathematics
2 marks
NAT
No negative marking

A sender (S) transmits a signal, which can be one of the two kinds: $H$ and $L$ with probabilities 0.1 and 0.9 respectively, to a receiver (R).

In the graph below, the weight of edge $(u, v)$ is the probability of receiving $v$ when $u$ is transmitted, where $u, v \in \{H, L\}$ . For example, the probability that the received signal is $L$ given the transmitted signal was $H$ , is 0.7.

If the received signal is $H$ , the probability that the transmitted signal was $H$ (rounded to 2 decimal places) is ________.

Channel diagram from sender S (H, L on the left) to receiver R (H, L on the right): H to H 0.3, H to L 0.7, L to H 0.8, L to L 0.2 — Tap the figure to enlarge

Try it: numerical answer: type the value

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Numerical answer. No negative marking.

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Answer: 0.04 (official GATE 2021 final answer key)

Concept used: Bayes' theorem: $P(\text{sent } H \mid \text{received } H) = \dfrac{P(H)\,P(H \to H)}{P(\text{received } H)}$ .

First step: $P(\text{received } H) = 0.1 \times 0.3 + 0.9 \times 0.8$ .

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Source: official GATE 2021 Set 1 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

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GATE CSE 2021 Set 1 Q64: Bayes' rule on a noisy two-signal channel

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