Exercise 1.30

Question

With definitions as in the previous problem, find the probability that a random n-letter word is a palindrome for $n = 7$ and for $n = 8$.

fifthist x · Accepted Answer

Suppose the word consists of $7$ letters. Once we choose the first letter, 
the seventh one has to be the same. Once we choose the second letter, the 
sixth one has to be the same. In general, we are free to choose $4$ letters. 
Hence, the probability that a $7$ letter word is a palindrome is 
$$\frac{24^{4}}{24^{7}} = \frac{1}{24^{3}}$$

If the word consists of $8$ letters, then there are $24^{8}$ possible words, 
but for a palindrome, the number of letters we are free to choose is still $4$. 
Hence, the probability is $$\frac{24^{4}}{24^{8}} = \frac{1}{24^{4}}$$

Exercise 1.30

Answers

Comments

Exercise 1.30

Answers

Comments

Add answer