Palindrome Action
What is the probability that a randomly chosen 4-digit palindrome number is divisible by ?
Note :- A palindrome number is such that it is the same written backwards, for example, 2002, 6886, etc.
The answer is 0.2.
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1 solution
Every 4-digit palindrome can be written as a b b a
a b b a = 1 0 0 1 a + 1 1 0 b
Now, 1001 is divisible by 7 , hence a can be anything(1,2,3...,9), but 110 and 7 are co-prime , thus b can only be 7 or 0.
Hence, the total number of divisible palindromes = (choices for a)×(choices for b)=9×2=18
Total palindromes = 9×10=90 (since a cant be 0)
Probability = 9 0 1 8 = 0 . 2