Problem on bsc with crossover probability

Question

Response to the following problem:

Consider a BSC with crossover probability of p. Suppose that R is the number of bits in a source codeword that represents one of 2^R possible levels at the output of a quantizer.

1. Determine the probability that a codeword transmitted over the BSC is received correctly.

2. Determine the probability of having at least one bit error in a codeword transmitted over the BSC.

3. Determine the probability of having ne or fewer bit errors in a codeword.

4. Evaluate the probabilities in parts 1, 2, and 3 for R = 5, p = 0.1, and ne = 5