UGC NET CSE | August 2016 | Part 2 | Question: 4

Question

What is the probability that a randomly selected bit string of length 10 is a palindrome ?

• A. $\frac{1}{64}$
• B. $\frac{1}{32}$
• C. $\frac{1}{8}$
• D. $\frac{1}{4}$

Answer 1

Option B is correct

we have to select 10 bits and with every bit we have two choice either 0 or 1 so the total no of 10 length bit strings are 2¹⁰

now in palindrome if we chose first 5 bits then our job is done as next 5 are fixed ( first 5 in reverse order)

0 or 1

0 or 1

0 or1

0 or1

0 or 1

fixed

fixed

fixed

fixed

fixed

So, for five bits can be chosen in 2⁵ (for every bit either 0 or 1).

Probability = 2⁵/2¹⁰ = 1/2⁵ = 1/ 32

Answer 2

With n length string we have 2^(n/2) bit string of pallindrome .so we have 2⁵= 32 bit strings of pallindrome and selecting at random from these will give probability of 2⁵/2¹⁰ =1/32

(B)option ans.