Final answer:
The probability that a marble with number 5 is blue is calculated by looking at the total number of marbles with that number, which is 1 blue and 1 red, making the probability 1/2. The options provided in the question do not contain the correct answer, as none of them is 1/2.
Step-by-step explanation:
The question is asking for the probability that a marble with the number 5 on it is blue, given that there are 3 red marbles labeled 1 to 3 and 11 blue marbles labeled 1 to 11. The total number of possible marbles with the number 5 is either a red or a blue marble, which adds up to 2 (1 red with number 5 and 1 blue with number 5). Since the marble selected has the number 5, we only focus on these two options.
To find the probability that the marble is blue, we need to calculate the number of favorable outcomes (the marble being blue with the number 5) divided by the total number of outcomes with number 5. The favorable outcome is 1 (only one blue marble has the number 5), and there are 2 possible outcomes (since there is a red marble and a blue marble both numbered 5), so the probability (P) is:
P(blue marble with number 5) = 1 (favorable outcome) / 2 (total outcomes) = 1/2.
Thus, the correct answer is not listed among the provided options (A, B, C, D). The actual probability is 1/2.