Question

Question: What is the probability that a randomly selected bit string of length \(11\) is a palindrome?

Short answer

Answer

The probability of a randomly selected bit string of length \(11\) is a palindrome \(\frac{1}{{32}}\).

Step-by-step solution

Answer

The probability of a randomly selected bit string of length \(11\) is a palindrome \(\frac{1}{{32}}\).

Concept of Probability 

Probability is simply how likely something is to happen. Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Formula:

The probability \( = \frac{{{\rm{ favorable outcomes }}}}{{{\rm{ total outcomes }}}}\)

Calculation for the probability that a bit string of length \(11\) is a palindrome 

The number of outcomes of string of length \(11\) is \({2^{11}}\).

The number of outcomes of palindrome bit strings is \({2^6}\).

If we randomly picked the one bit, the probability is \(\frac{{{2^6}}}{{{2^{11}}}} = \frac{1}{{32}}\).

Therefore, the probability of a randomly selected bit string of length \(11\) is a palindrome \(\frac{1}{{32}}\).