Consider a binary code with 6 bits (0 or 1) in each code word. An example of a c

Question

Consider a binary code with 6 bits (0 or 1) in each code word. An example of a code word is 010010. a. How many different code words are there? b. How many code words have exactly three 0’s? c. In each code word a bit is a 0 with probability 0.8, independent of any other bit, what is the probability of observing the code 001111. d. What is the probability that the code word will contain exactly three zeros (Hint: The way that you would read this statement is the P[observing exactly three zeros] = P[000111] + P[100011] + etc …, as you can see there are so many ways you could observe 3 zeros in a code, use the combinatorics principle to help you find the probability in this question )

Explanation / Answer

Answer:

a. How many different code words are there?

b. How many code words have exactly three 0’s?

c. In each code word a bit is a 0 with probability 0.8, independent of any other bit, what is the probability of observing the code 001111.

d. What is the probability that the code word will contain exactly three zeros

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