**Question:** You are given two bitstrings a1, a2, .. a77 and b1, b2, .. b77 of length 77 In both bitstrings, each bit is 0 with **probability 3/4**, and 1 with **probability 1/4** (independent of all other bits).

Consider the string: a1-b1, a2-b2, ..., a77-b77.

What is the probability that each element in this string is non-zero?

**Answer: 1.586381421\*10^-33**

**Attempt:**

Non-zero probability is 1/4 for both bitstrings.
If both bitstrings are subtracted by one another for length 77, then it shouldn't it be (1/4)\*(1/4) = 1/16 be the probability of the new string being non-zero

Total number of possible bitstrings = 2^77

Probability: 1/16/2^77 = 4.13\*10^-25