A jar has 19 marbles and 5 of them are green. You pull 3 marbles without replacement. What is the probability that all are green?
To calculate the probability that all 3 marbles pulled are green, we need to first determine the total number of possible outcomes when pulling 3 marbles from the jar without replacement.
There are 19 marbles in total, so the number of ways to choose 3 marbles from 19 is given by the combination formula:
nCr = n! / [r!(n-r)!]
19C3 = 19! / [3!(19-3)!]
19C3 = 19! / (3! * 16!)
19C3 = (19 * 18 * 17) / (3 * 2 * 1)
19C3 = 969
Now, we need to determine the number of ways to choose 3 green marbles from the 5 green marbles in the jar:
5C3 = 5! / [3!(5-3)!]
5C3 = 5! / (3! * 2!)
5C3 = (5 * 4 * 3) / (3 * 2 * 1)
5C3 = 10
Therefore, the probability of pulling 3 green marbles from the jar is:
P(all 3 marbles are green) = 5C3 / 19C3
P(all 3 marbles are green) = 10 / 969
P(all 3 marbles are green) ≈ 0.0103
So, the probability that all 3 marbles pulled are green is approximately 0.0103 or 1.03%.