Hannah is instructed to write down a positive, 4-digit integer. what is the probability it is an even palindrome (a number that reads the same forward and backward)? express your answer as a common fraction.

Hence, the answer is:

                    1/100

The total number of 4 digit numbers that are possible are:

                         9000

(   Since at the first place except zero any of the number 1-9 are possible i.e. we have 9 choices.

at the second, third and fourth place any of the number between 0-9 are possible i.e. we have 10 choices.

Hence, the total number of cases are:

                  9×10×10×10=9000  )

Also, the number of possibility that the number is an even palindrome is: 90

( Since at the first place if a number is chosen then we need not have to chose the last number and for the first place we have nine choices.

and similarly if a number is chosen at the second place then we need not have to chose for the third place as the second and third place numbers would be same and for the second place we have 10 choices (0-9)

Hence, the number of such cases are:

              9×10×1×1=90 )

Hence, the probability that the number is an even palindrome is:

                     90/9000=1/100