The probability of picking a purple marble and spinning green is 1/9.
To find the probability of picking a purple marble and spinning green, we need to consider the total number of marbles and the number of purple and green marbles.
In this case, the bag contains four green marbles, three red marbles, and two yellow marbles.
To find the probability of drawing a yellow marble and then a green marble, we multiply the probability of drawing a yellow marble (2/9) by the probability of spinning a green marble (4/8) after drawing a yellow marble.
So, the probability of picking a purple marble and spinning green is:
(2/9) * (4/8) = 8/72 = 1/9