1 votes 1 votes 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 Sanjay Sharma asked Mar 9, 2017 Sanjay Sharma 2.8k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 6 votes 6 votes 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 . Required Probability = $\frac{2^5}{2^{10}} = \frac{1}{2^{5}}$ Kapil answered Mar 9, 2017 • selected Mar 9, 2017 by rude Kapil comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes 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. jatin saini answered Mar 9, 2017 jatin saini comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes 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 = $\frac{1}{32}$. dd answered Mar 9, 2017 dd comment Share Follow See all 0 reply Please log in or register to add a comment.