Final answer:
The probability of first picking a green marble, replacing it, and then picking a blue marble from a bag containing 5 red, 4 green, and 3 blue marbles is 1/12.
Step-by-step explanation:
The question is about calculating the probability of selecting a green marble and then a blue marble from a bag with a replacement in between the picks. The process involves two independent events since the green marble is replaced before picking the blue marble.
To calculate the probability of picking a green marble first, we consider the total number of marbles and the number of green marbles. Given there are 5 red, 4 green, and 3 blue marbles, the total number of marbles is 5+4+3=12. The probability of picking a green marble is thus 4/12 or 1/3. Because we replace the green marble, the bag's contents remain the same for the second pick.
The probability of picking a blue marble after replacing the green marble is therefore based on the same total of 12 marbles. The probability is 3/12 or 1/4. Now, since these are independent events, we multiply the two probabilities together to get the overall probability of both events happening in sequence: (1/3) * (1/4) = 1/12.
In summary, the probability of first picking a green marble, replacing it, and then picking a blue marble is 1/12.