Question

Two six-sided dice each have the numbers 1 through 6 on their faces. Neither die is fair, but they are both weighted the same. The probability of rolling a certain number on one die is given in the table below:

# 1 2 3 4 5 6
probability 1/6 1/6 1/9 ? 2/9 ?

If the probability that the two dice both show the same numbers is (2/3)^4, we can express the probability of rolling 10 on these two dice as a/b where a and b are coprime positive integers. What is the value of a+b?

Answer 1

163.