To solve this problem, we can use the concept of probability. The probability of an event happening is defined as the number of favorable outcomes divided by the total number of possible outcomes.

Let's break the problem down step by step:

Step 1: Determine the total number of possible outcomes.
- In this case, we are picking three marbles from the urn, so the total number of possible outcomes is given by the combination formula: C(7, 3) = 7! / (3! * (7-3)!) = 35.

Step 2: Determine the number of favorable outcomes.
- To have two green marbles and one red marble, we need to consider the different ways this can happen.
- We can have green-green-red, green-red-green, or red-green-green. Let's calculate the number of favorable outcomes for each case.

Case 1: Green-Green-Red
- There are 4 green marbles and we need to pick 2 of them, so the number of ways to do this is given by the combination formula: C(4, 2) = 4! / (2! * (4-2)!) = 6.
- There is only 1 red marble left, so the number of ways to pick it is 1.

Case 2: Green-Red-Green
- There are 4 green marbles and we need to pick 1 of them, so the number of ways to do this is given by the combination formula: C(4, 1) = 4! / (1! * (4-1)!) = 4.
- There are 3 red marbles left and we need to pick 1 of them, so the number of ways to do this is given by the combination formula: C(3, 1) = 3! / (1! * (3-1)!) = 3.

Case 3: Red-Green-Green
- There are 3 red marbles and we need to pick 1 of them, so the number of ways to do this is given by the combination formula: C(3, 1) = 3! / (1! * (3-1)!) = 3.
- There are 4 green marbles left and we need to pick 2 of them, so the number of ways to do this is given by the combination formula: C(4, 2) = 4! / (2! * (4-2)!) = 6.

Step 3: Calculate the probability.
- The number of favorable outcomes is the sum of the favorable outcomes for each case: 6 + 1 + 4 + 3 + 3 + 6 = 23.
- The probability is given by the number of favorable outcomes divided by the total number of possible outcomes: 23/35.

Therefore, the correct answer is option B) 18/35.