refer to a bag of marbles containing 5 green marbles, 4 red marbles and 2 yellow marbles. Three marbles are drawn from the bag, without replacement. What is the probabilty that all three marbles drawn are green?

11 marbles, 5 green

probability that #1 is green = 5/11

now 10 marbles, 4 green
probability that #2 is green = 4/10

now 9 marbles, 3 green
probability that #3 is green = 3/9

so
5/11 * 2/5 * 1/3
= 2/33

thanks what is the probability that at least one of the marbles drawn is green? I thinks it's 1/11 but not sure.

Then what is the probability that only one of the marbles drawn are green?

To find the probability of drawing three green marbles from the bag, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of marbles in the bag = 5 green marbles + 4 red marbles + 2 yellow marbles = 11 marbles

When we draw the first marble, there are 11 marbles to choose from, and since we want a green marble, there are 5 green marbles as favorable outcomes.

Now, after drawing the first green marble, there are 10 marbles left in the bag (4 red marbles + 1 green marble + 2 yellow marbles). Therefore, for the second draw, there are now 10 marbles to choose from, with 4 green marbles as favorable outcomes.

Finally, after the second green marble is drawn, there are 9 marbles left in the bag (3 green marbles + 4 red marbles + 2 yellow marbles). So, for the third draw, there are 9 marbles to choose from, with 3 green marbles as favorable outcomes.

Therefore, the number of favorable outcomes for drawing three green marbles is 5 * 4 * 3 = 60.

Now, to find the total number of possible outcomes for drawing three marbles without replacement, we need to calculate the number of ways to choose 3 marbles out of the 11 in the bag.

The number of ways to choose 3 marbles out of 11 is given by the combination formula: C(11,3) = 11! / (3! * (11-3)!) = 165.

Therefore, the probability of drawing three green marbles is: favorable outcomes / total outcomes = 60 / 165 ≈ 0.3636 (rounded to four decimal places) or 36.36% (rounded to two decimal places).

So, the probability that all three marbles drawn are green is approximately 0.3636 or 36.36%.