Final answer:
To find the probability of randomly choosing a red and then a green marble from a jar, multiply the probabilities of each event happening.
Step-by-step explanation:
To find the probability of randomly choosing a red and then a green marble from the jar, we need to consider the total number of marbles and the number of red and green marbles. There are 20 marbles in total: 3 green, 12 blue, and 5 red. When we select a red marble from the jar, we keep it. So the probability of choosing a red marble is 5/20. After selecting a red marble, there are now 19 marbles left in the jar: 3 green, 12 blue, and 4 red. The probability of selecting a green marble from the remaining marbles is 3/19. To find the overall probability of both events happening, we multiply the probabilities together: (5/20) x (3/19) = 15/380 = 3/76. Therefore, the correct answer is not listed among the given options.