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# A palindrome integer is an integer that reads the same backward as for

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Manager
Joined: 07 Jun 2018
Posts: 51
Location: United States
A palindrome integer is an integer that reads the same backward as for  [#permalink]

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14 Jan 2019, 23:49
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Difficulty:

25% (medium)

Question Stats:

69% (01:29) correct 31% (02:17) wrong based on 33 sessions

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A palindrome integer is an integer that reads the same backward as forwards. If a sample space contains all palindrome integers of 5 digits, what is the probability that an arbitrarily chosen integer is an even palindrome?

1. 1/4
2. 4/9
3. 1/2
4. 5/9
5. 3/5
Math Expert
Joined: 02 Aug 2009
Posts: 7989
Re: A palindrome integer is an integer that reads the same backward as for  [#permalink]

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15 Jan 2019, 00:08
2
Jazzmin wrote:
A palindrome integer is an integer that reads the same backward as forwards. If a sample space contains all palindrome integers of 5 digits, what is the probability that an arbitrarily chosen integer is an even palindrome?

1. 1/4
2. 4/9
3. 1/2
4. 5/9
5. 3/5

Normally choosing an even or an odd units digit should be 1/2, as the probability of choosing any of them is same.
However, here we are talking of a 5-digit number, and the number is of the form ABCBA, so A cannot be 0 as it will become a 4-digit number and A will define if the number is odd or even

Therefore, we are left with 9 ways, 1 to 9, to fill up A, out of 9, 4 are even - 2, 4, 6, 8 and rest are odd..
so probability to pick even palindrome is $$\frac{ways-to-pick-even-digit -for-A}{total-ways}=\frac{4C1}{9C1}=\frac{4}{9}$$

B
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Re: A palindrome integer is an integer that reads the same backward as for   [#permalink] 15 Jan 2019, 00:08
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