Final answer:
The probability of drawing a yellow marble and then a green marble from a bag without replacement is 27/200 or approximately 0.135.
Step-by-step explanation:
The probability of drawing a yellow marble and then a green marble from a bag without replacement can be calculated as follows:
First, we calculate the probability of drawing a yellow marble on the first draw. There are 12 yellow marbles out of a total of 12+5+14+9 = 40 marbles in the bag.
So, the probability is 12/40.
Next, we calculate the probability of drawing a green marble on the second draw. After drawing a yellow marble, there are 11 yellow marbles and 9 green marbles left in the bag.
So, the probability is 9/20.
To find the probability of both events happening together, we multiply the probabilities: (12/40) × (9/20) = 27/200 or approximately 0.135.