I don't think you are interpreting the problem correctly. the problem never said you had to keep picking until you ended up with the "combination". It simply says, if you were to pick 3 balls (with replacement) what is the probability that you will pick a red, then a green, then a blue.I roughly have the answers of these ones, but I can't find a correct way to explain everything...
We have a total of 15 balls in a box : 6 red, 5 green and 4 blue.
1) We assume that we pick balls one by one and any taken balls will be put back in the box. What is the probability of getting, in this order, a red ball, then a green, then a blue one ?
The way of doing is blurry to me, but I understood it this way : we take a ball and if it's not red, we put it back. And we continue as long as we get a red ball.
We keep this ball, and we go on.
The answer is something like .
The probability of picking a red ball is:
that is, you can choose 1 of 6 possible choices as there are 6 red balls, out of 15 total choices. so there are 6 ways out of 15 to get a red ball.
Since the ball is replaced, when choosing the next ball, you still have 15 total choices, of which you must choose 1. So the probabilities for choosing a green and blue ball are: and , respectively.
Since each choice is independent, the probability of all three happening is just the product of the probabilities, that is:
For "without replacement": after picking each ball, the total remaining choices decrease by 1. So after picking the red, there are 14 balls from which to choose the green, then 13 from which to choose the blue. hence this probability is:2) We assume then that we don't put back the balls once they're taken, and we're looking for the same probability.
I must say I have no idea for this one, I struggle to represent the situation...
Please help This is no assignment or anything, I'm just helping someone and got stuck to these questions