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Official PYQ · 2025Set 1 · Q46Data Link Layer: Framing, Error Detection, MAC, Ethernet BridgingNAT2 marks

GATE CS 2025 Set 1 Q46 — Data Link Layer: Framing, Error Detection, MAC, Ethernet Bridging

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Suppose a 55-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 0.010.01. 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)
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Answer: 0.949:0.952

To find the probability that the 55-bit message is delivered error-free, we can model the transmission of each bit as an independent Bernoulli trial.

Let:

  • p=0.01p = 0.01 be the probability that a bit gets flipped (error).
  • q=1−p=0.99q = 1 - p = 0.99 be the probability that a bit is transmitted correctly (error-free).

Since the flipping of each bit is independent of the others, the probability that all 55 bits in the message are transmitted without any error is given by:

P(Error-free message)=q5=(0.99)5P(\text{Error-free message}) = q^5 = (0.99)^5

Calculating this value:

(0.99)5≈0.95099(0.99)^5 \approx 0.95099

Rounding off to three decimal places, we get:

P(Error-free message)≈0.951P(\text{Error-free message}) \approx 0.951

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