As Plato pointed out, I made a mistake and overlooked your problem said, 'each digit appears once'. Instead of deleting it, let's just say this is the case where the digits repeat.
1) A five-digit number is created using the digits 1-5 each once. What is the probability that the number is odd? Express your answer as a common fraction.
2) The sum of the digits of a number is 9. What is the
probability that the number is prime?