Computer Sciences > GATE 2025 SET-1 > Error Control
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)
Correct : 0.951
The correct answer is 0.951.
Each bit has a probability of 0.01 of getting flipped, which means each bit is transmitted correctly with probability 1 - 0.01 = 0.99.
Since the flipping of each bit is independent of the others, the probability that all 5 bits are received without any error is simply the product of the individual success probabilities:
P(error-free) = (0.99)5 = 0.9509900499
Rounded to three decimal places: 0.951.
This is a direct application of the multiplication rule for independent events - when all outcomes must occur together and they are independent, we multiply their individual probabilities.
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