I look at a random time of day at a digital clock that shows times from 1:00 through 12:59. if i ignore the colon, what is the probability that the digits display a palindrome such as 8:08? express your answer as a common fraction.

The probability that the digits display a palindrome = 19/240 Ans.

As we know the total no. of possible hours = 12

Total number of possible minutes = 60

Therefore, total no. of possible times that can be shown are = 12

Since total no. of Palindromes possible per hour for the nine hours 1 through 9 = 6

No. of palindromes per hour from 10 through 12 = 1

Therefore, total no of palindromes = (6*9) + 3 = 57

Probability that the digits display a palindrome = 57/720 = 19/240