Final answer:
The probability of rolling a 5 given that the number rolled is a prime number is 1/3, since there are three prime numbers on a six-sided die {2, 3, 5} and only one of them is a 5.
Step-by-step explanation:
The question asks for the probability of rolling a 5, given that we have rolled a prime number on a six-sided die. There are three prime numbers on a six-sided die: {2, 3, 5}. Since these are the only prime numbers we could have rolled, and the event specifies that we did roll a prime, we now only consider these numbers as possible outcomes.
Now, we are interested in the probability that the number rolled is specifically a 5 among the prime numbers {2, 3, 5}. There is only one '5' in the set of prime outcomes, so the probability is 1 out of 3. Thus, the correct answer is 1/3, which corresponds to option B.