Please circle the answer which seem most correct. Also, Please show work.

1. Assuming that we have a binary symmetric channel (the probability of switching 1 to 0 is the same as the probability of switching a 0 to a 1), what is the probability that exactly r errors will be made in transmitting a bit string of length n? The probability of a bit error is p.

a.

b.

c. you can not find it with the given information

d.

2. Suppose that p=.01, what is the probability of no errors in a 4-bit message?

a. 0.960596 b. 1.960596

c. 4 d. 0.01

3. What is the probability of one error in a 4-bit message?

a. 0.038812 b. 0.01

c. 0.5 d. 0.76