Each die is a standard 6-sided cube, but the six faces bear the first six numbers of the Fibonacci sequence, 1, 1, 2, 3, 5, and 8. If this pair of dice is rolled once, what is the probability that the sum of the numbers showing on the top faces of the two dice is a Fibonacci number?

Each die is a standard 6-sided cube, but the six faces bear the first six numbers of the Fibonacci sequence, 1, 1, 2, 3, 5, and 8. If this pair of dice is rolled once, what is the probability that the sum of the numbers showing on the top faces of the two dice is a Fibonacci number?