To determine the probability of drawing a blue marble from a bag containing 5 blue marbles and 7 green marbles, we need to follow these steps:
1. Calculate the total number of marbles in the bag: Add the number of blue marbles to the number of green marbles.
[tex]\[
\text{Total marbles} = \text{Number of blue marbles} + \text{Number of green marbles} = 5 + 7 = 12
\][/tex]
2. Determine the probability of drawing a blue marble: The probability of an event is defined as the ratio of the favorable outcomes to the total number of possible outcomes. In this case, the favorable outcome is drawing a blue marble.
[tex]\[
\text{Probability of drawing a blue marble} = \frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{5}{12}
\][/tex]
Based on these calculations, the probability of drawing a blue marble from the bag is given by option d:
[tex]\[
\boxed{\frac{5}{12}}
\][/tex]
