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)
Answer
0.95
Explanation
The message arrives error-free only if none of its 5 bits flips. Each bit survives with probability \(1 - 0.01 = 0.99\), and the bits are independent, so the probabilities multiply.
\[P = (0.99)^5 = 0.95099 \approx 0.951\]
Answer: 0.951