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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.

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

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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?)

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It would be clearer to ask "How many bits can you choose...". – Austin Mohr Nov 15 '12 at 2:19
C'est vrai, Austin, but I am trying to offer the gentlest possible hint. – ncmathsadist Nov 15 '12 at 2:37

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

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