Final answer:
The probability that a two-digit prime number's digits sum to 9 is 1/10 or 0.1.
Step-by-step explanation:
The probability that a two-digit prime number's digits sum to 9 can be determined by finding the number of two-digit prime numbers whose digits sum to 9 and dividing that by the total number of two-digit prime numbers.
There are two two-digit prime numbers whose digits sum to 9: 18 and 81.
Therefore, the numerator is 2.
The total number of two-digit prime numbers is 20 (11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89).
So, the probability is 2/20, which simplifies to 1/10 or 0.1.