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I have been trying this problem for awhile now but i cant get it. Can someone please help?

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.

Aug 7, 2019

#1
+106533
+2

Even plaindromes

Starts  with                        Ends with

2                                         2

4                                         4

6                                         6

8                                         8

We have 10  choices for the middle two numbers  in each case   = 40  possibiliities

We have   90   4 digit palindromes   (the other 50  come from starting and ending the number with 1,3,5,7, or 9....and for each of these we have  10 possibiliites)

So....the  probability of an even palindrome  =   40  / 90    = 4 / 9

Aug 7, 2019
#2
+1

I am sorry but this is incorrect

Guest Aug 7, 2019
#3
+1

He is right, this is not correct. I have looked through your work however, and I can't see what you did wrong.

Guest Aug 7, 2019
#4
+106963
+2

CPhill has found the probability that it is an even palidrome given that it is a palindrome.

I do think think this is quite what the question is asking.

I think it wants the probability that it is a 4 digit even palidrone given that it is a 4 digit number.

The number of 4 digit numbers is 9*10*10*10 = 9000

4/900

Aug 7, 2019
#5
+106533
+1

Yes....Melody's answer is  correct.....I didn't account for the  fact that we want the ratio of even palindormes 4-digit palindromes to ALL 4-digit  integers...

Thanks, Melody!!!!

CPhill  Aug 8, 2019