Short answer: 14/81
There is a 2/9 chance of picking a green marble the first time.
Since this leaves 8 marbles (only one of which is green; you took the other one), that leaves an 7/8 chance of picking any other colour the second time.
To find the overall probability, you simply multiply the two values (2/9 * 7/8 = 14/81). This is simple to understand. You can only get a green marble every 2 out of 9 tries. For each of these 2 times, you have a 7/8 chance of getting a different colour the second time. So, you have a 7/8 chance every 2/9 times. Simply multiply them to get the total number of possibilities.
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