HR has 19 marbles and five of them are green. You pull three marbles without replacement. What is the probability that all are green
To find the probability that all three marbles are green, we need to calculate the probability of selecting a green marble on the first draw, then a green marble on the second draw, and finally a green marble on the third draw.
The probability of first drawing a green marble is 5/19.
After drawing a green marble, there are now 4 green marbles left and a total of 18 marbles remaining. So the probability of drawing a green marble on the second draw is 4/18 (or simplifying, 2/9).
After drawing two green marbles, there are 3 green marbles left and 17 marbles remaining. So the probability of drawing a green marble on the third draw is 3/17.
Now, we multiply the probabilities of each draw to get the overall probability of pulling three green marbles:
(5/19) * (4/18) * (3/17) = 0.0174
Therefore, the probability of pulling all green marbles on the three draws is 0.0174 or 1.74%.