Question

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.

Answer 1

Answer:

19/240

Step-by-step explanation:

First, we compute the total number of possible times that can show. There are 12 possible hours, and 60 possible minutes, so the total number of possible times is 12 * 60 = 720.

Now we compute the number of palindromes. There are 6 palindromes per hour for the nine hours 1 through 9 (1:01, 1:11, 1:21, 1:31, 1:41, 1:51 for example). There is one palindrome per hour from 10 through 12, namely 10:01, 11:11, and 12:21. Hence, the number of palindromes is 6 * 9 + 3 = 57.

Therefore, the probability that the time is a palindrome is 57/720 = 19/240.

Answer 2

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