To find the probability that a randomly selected marble is blue from a bag containing red, blue, and green marbles, follow these steps:
1. Determine the total number of marbles in the bag:
- Number of red marbles: 6
- Number of blue marbles: 7
- Number of green marbles: 4
So, the total number of marbles is:
[tex]\[
6 + 7 + 4 = 17
\][/tex]
2. Identify the number of blue marbles: There are 7 blue marbles.
3. Calculate the probability of selecting a blue marble: The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
In this case, the favorable outcome is selecting a blue marble, and the total number of possible outcomes is the total number of marbles in the bag.
Hence, the probability of selecting a blue marble is:
[tex]\[
\frac{\text{Number of blue marbles}}{\text{Total number of marbles}} = \frac{7}{17}
\][/tex]
So, the probability that a randomly selected marble is blue is:
[tex]\[
\frac{7}{17}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{7}{17}}
\][/tex]
