GATE CS 2025 Set 1 Q.56: Data Link Layer: Framing, Error Detection and Sliding Window

Suppose a 5-bit message is transmitted from a source to a destination through a noisy channel. The probability that a bit of the message gets flipped during transmission is $0.01$ . Flipping of each bit is independent of one another. The probability that the message is delivered error-free to the destination is ______ . (rounded off to three decimal places)

Your answer

Official answer and solution

Accepted answers: 0.949 to 0.952
From: Official GATE 2025 answer key

Solution

Compute $(1 - p)^5$ where $p = 0.01$ is the independent bit-flip probability.

For the 5-bit message to be delivered completely error-free, none of the 5 bits may flip. Since each bit is transmitted without error with probability $1 - 0.01 = 0.99$ independently:

P(\text{error-free}) = (0.99)^5 \approx 0.9509900499 \approx 0.951

Final answer

0.951

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2025 Computer Science and Information Technology - Session 1 (CS1)
Question: 56 of 65
Section: Computer Science and Information Technology

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