Probability of palindrome of length 11

Question

What is the probability that a random bit string of length 11 is a palindrome?

Anyone have an idea of how to do this? I'm not sure how to calculate the different cases.

Answer 1

There are 2048 arbitrary bit strings of length 11. Now count the pallindromic ones. (How many can you choose arbitarily so the rest is determined?)

Answer 2

Hint: you need $b_i = b_{12-i}$ for $i = 1$ to $5$.

Answer 3

the first 6 bits don't matter, as stated earlier b1 = b11 etc Pallidromic=1/2 * 1/2 * 1/2 * 1/2 * 1/2