# Probability that 2 identical binomial experiments are within an interval of each other

Homework had this question. Part a is relatively straightforward, as it's a cdf of the function. For part b I could write a script that will compute all possible sets and divide by the total sets, but how would I solve this problem in an efficient way?

A binary communication channel transmits a sequence of "bits" (0s and 1s). Suppose that for any particular bit transmitted, there is a 15% chance of a transmission error (a 0 becoming a 1 or a 1 becoming a 0). Assume that bit errors occur independently of one another. (Round your answers to four decimal places.)

(a) Consider transmitting 1000 bits. What is the approximate probability that at most 175 transmission errors occur?

.9868