That is1001a+110b.

According to the property that an integer can be divisible by 7, if the single digit of an integer is truncated, then the remaining number is subtracted by twice this single digit. If the difference is a multiple of 7, the original number can be divisible by 7.

So as long as100a+11b-2a = 98a+11b is divisible by 7, palindromes can be divisible by 7.

If 98 is divisible by 7, then this question has nothing to do with A.

So as long as 1 1b can be divisible by 7, it can meet the requirements of B.

B has 10 selection methods, among which 1 1b can be divisible by 7 when choosing 0 or 7.

So the probability is 2/ 10= 1/5.