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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)

1. 0.9509900499
2. 0.96059601
3. 0.904382075
4. 0.990000000

Correct answer: 0.9509900499

Solution

Each bit is correct with probability 0.99 and bits are independent, so the message is error-free with probability 0.99^5 = 0.95099. The stored answer 0.96059601 is 0.99^4 (only 4 bits) and is wrong; the correct value is option 0.

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