Question: 2018 Winter Final - 14
You are given two bitstrings $a_1,a_2,\dots,a_{77}$ and $b_1,b_2,\dots,b_{77}$ 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 $$ a_1-b_1,a_2-b_2,\dots,a_{77}-b_{77}. $$ What is the probability that each element in this string is non-zero?
Consider the string $$ a_1-b_1,a_2-b_2,\dots,a_{77}-b_{77}. $$ What is the probability that each element in this string is non-zero?
(a)
$(3/8)^{77}$
(b)
$(4/8)^{77}$
(c)
$(5/8)^{77}$
(d)
$(6/8)^{77}$