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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
avatar+104937 
+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

 

 

cool cool cool

 Aug 7, 2019
 #2
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+1

I am sorry but this is incorrect

Guest Aug 7, 2019
 #3
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+1

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

Guest Aug 7, 2019
 #4
avatar+105689 
+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

 

The answer I believe is 

 

4/900

 Aug 7, 2019
 #5
avatar+104937 
+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!!!!

 

 

cool cool cool

CPhill  Aug 8, 2019

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