What is the probability that a randomly selected bit string of length 10 is a…
2016
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.
\(\frac 1 4\)
Attempted by 12 students.
Show answer & explanation
Correct answer: B
Quick answer: 1/32
Explanation:
Total number of bit strings of length 10: 2^10 = 1024.
Number of palindromic bit strings: a length-10 palindrome is fully determined by its first 5 bits because each of the last 5 bits must mirror the first 5, so there are 2^5 = 32 palindromes.
Probability = number of palindromes / total = 32 / 1024 = 1/32.