Came across this problem, and while i know the correct answer, I cannot seem to rationalize it.
Given 2 bit strings that are generated randomly , where each bit is either 0 or 1 (eg 001010101010). What is the probability that the bit at a specific place will equal the bit in the same place in the other string?
Now, the correct answer is noticing that there are only four possible combinations for this; 00, 01, 10, 11 , where only two of them lead the numbers being the same. Thus the answer is 1/2
However, the way that I think about this, is to say, the probability that the bit in string 1 will be a certain number is 1/2, the probability that the bit in the other string will be 1/2 , so 1/4.
Or using the formula , two random integers are equal in a range [m,n]
1/(n-m+1)*(n-m+1) = 1/(2)(2) = 1/4
Can someone help me rationalize this