Final answer:
The probability of drawing a blue marble followed by a green marble from the urn without replacement is 2/15.
Step-by-step explanation:
The student's question pertains to the probability of drawing two marbles of specific colors in succession without replacement from an urn containing 4 green, 3 blue, and 3 red marbles. To find the probability of drawing a blue marble followed by a green marble, we calculate the probability of each event independently and then multiply the probabilities since the events are sequential and dependent.
First, the probability of drawing a blue marble is the number of blue marbles over the total number of marbles, which is 3/10. Once a blue marble is drawn, we do not replace it, thus the total number of marbles reduces to 9, and green marbles are still 4. So, the probability of drawing a green marble after drawing a blue one is now 4/9.
The combined probability of both events occurring in sequence is the product of the individual probabilities:
Probability of blue then green = (First Event Probability) × (Second Event Probability) = (3/10) × (4/9).
To get the final probability, simply multiply the two fractions:
Final Probability = (3/10) × (4/9) = 12/90 = 2/15 after simplifying the fraction.