Final answer:
To calculate the probability of drawing three red marbles without replacement from a box containing 8 red and 12 green marbles, multiply the probabilities of drawing a red marble on each selection: (8/20) * (7/19) * (6/18) = 7/95.
Step-by-step explanation:
The student is seeking the probability that all three marbles drawn from the box are not green given that there are 8 red and 12 green marbles in total. To find this probability, we need to calculate the chances of drawing red marbles consecutively without replacement.
On the first draw, the probability of drawing a red marble is 8/20. Assuming a red marble is drawn, there are now 7 red and 12 green marbles left, so the probability of drawing another red on the second draw is 7/19. If another red marble is drawn, there are 6 red and 12 green marbles left, so the probability of drawing another red on the third draw is 6/18 or 1/3. Multiplying these probabilities gives the overall probability of drawing three red marbles without replacement:
(8/20) * (7/19) * (6/18) = (7/95)
Therefore, the probability that none of the three marbles drawn are green is 7/95.