Final answer:
The probability of drawing three red marbles without any green marbles is 14/285.
Step-by-step explanation:
To find the probability that none of the marbles drawn are green, we need to calculate the probability of drawing a red marble on each of the three draws. The probability of drawing a red marble on the first draw is:
P(red on 1st draw) = number of red marbles / total number of marbles = 8/20 = 2/5
Since marbles are drawn without replacement, the probability of drawing a red marble on the second draw is:
P(red on 2nd draw) = number of remaining red marbles / remaining total number of marbles = 7/19
Similarly, the probability of drawing a red marble on the third draw is:
P(red on 3rd draw) = 6/18 = 1/3
To find the probability of all three events happening, we multiply the individual probabilities:
P(none of them are green) = P(red on 1st draw) x P(red on 2nd draw) x P(red on 3rd draw) = (2/5) x (7/19) x (1/3) = 14/285.