Question

Suppose that 1% of (binary) bits received by your smartphone have errors. What is the probability that the 28th bit received by your smartphone is the first erroneous bit

Answer 1

Probabilities are used to determine the chances of events

The probability that the first erroneous bit is the 28 bit is 0.0076

How to determine the probability

The given parameter is:

p =1% --- the probability that a bit has errors

The probability that the first erroneous bit is the 28 bit means that the first 27 bits do not have errors.

So, we have:

$Pr = (1 - p)^{27} * p$

The equation becomes

$Pr = (1 - 1\%)^{27} * 1\%$

Evaluate

$Pr = 0.0076$

Hence, the probability that the first erroneous bit is the 28 bit is 0.0076

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