Question

what is the probability that a randomly chosen bit string of length  10 is palindrome

a)1/64   b)1/32   c) 1/8   d)1/4

Answer 1

• Total number of bit-strings of length $10$ possible = $2^{10}$
• To make a string palindrome, we only care about first half digits and rest of them are just replicated .
• Hence, here we care of first $5$ digits only in $2^{5}$ ways and rest $5$ are replicated in only $1$ way .

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Required Probability = $\frac{2^5}{2^{10}} = \frac{1}{2^{5}}$

Answer 2

Ans B)1/32

           first five bits can be anythink,total of 32 combinations and last 5 bits are just reverse of them.

           Total combinations of 10 bits are=1024

           Total palindromes=32

           Probablity that randomly chosen string is palindrome=32/1024=1/32.

           

            

Answer 3

To get a palindrome we can toggle the bits in only one-half of the $10$ length string.

So,

• Number of favourable cases = Number of palindrome bit strings of length $10$ = $2^5 = 32$
• Total Strings of length $10$ = $2^{10} = 1024$ 
• Answer = $\frac{1}{32}$.