Assume that there is a random bit sequence generator that each time returns a bit sequence of length 100. Each bit of the sequence can be a 1 or 0 with equal probability.
Question: What is the probability that two bit sequences taken from the generator match in more than 60% of the bits?
Attempted Solution:
Taking influence from this answer:
robjohn (https://math.stackexchange.com/users/13854/robjohn), Probability that two numbers differ by one bit, URL (version: 2015-07-28): https://math.stackexchange.com/q/1376557
, I figured the answer would be:
$\frac {\sum_{i=0}^{39} {{100} \choose {i}} } {2^{100}}$
However, I am not sure if this answer is correct since I did not make use of the given probability for each bit.