The “a-number” of a number x is defined as the ones digit of 2^x. Antony rolls a die with 6 sides labeled with the integers from 1 to 6, each of which has an equal probability of landing face-up. He then takes 3^a, where a is the a-number of the result of his die roll, and plots 3^a on a number line as the point A. Finally, he repeats this entire process, this time plotting the result as the point B. What is the probability that the distance between A and B is greater than the value of B?	Choose the correct answer:
A) 3 / 8  B) 13 / 36  C) 17 / 36  D) 19 / 36  E) 23 / 36

Rationale: if you calculate 3 ^ a for 1 st roll , all 6 results will be 9 , 81 , 6561 , 729 , 9 , 81 . this result is the same for 2 nd roll . 9 , 81 , 6561 , 729 , 9 , 81 . about distance : if the first result is 9 and the second is also 9 , the distance is 9 - 9 = 0 which is smaller than 9 . if the first result is 9 and the second is 81 , the distance is 81 - 9 = 72 which is also smaller than b which has the value of 81 . if the first result is 81 and the second is 9 , the distance will be greater than b . distance 81 - 9 = 72 > 9 . on the first roll , the probability of getting result 9 is 2 / 6 . in this case no other alternative values for second roll which would make the distance greater than b . so probability is 0 . so next estimations are : probability of getting 81 on the first roll ( 2 / 6 ) * probability of getting 9 on the second roll ( 2 / 6 ) = 1 / 9 probability of getting 729 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 on the second roll ( 4 / 6 ) = 1 / 9 probability of getting 6561 on the first roll ( 1 / 6 ) * probability of getting 9 , 81 , 729 on the first roll ( 5 / 6 ) = 5 / 36 all together : 1 / 9 + 1 / 9 + 5 / 36 = 13 / 36 = b
Answer: B