Answer:
0.7738 = 77.38% probability that an incorrect message is received.
Step-by-step explanation:
For each bit, there are only two possible outcomes. Either it is corrupted, or it is not. The probability of a bit being corrupted is independent of any other bit. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
5% probability a bit is sent incorrectly:
This means that
Message of length 5
This means that
What is the probability that an incorrect message is received?
This is the probability of at least one incorrect bit, which is:
In which
0.7738 = 77.38% probability that an incorrect message is received.