Given a bag containing 20 marbles of 5 different colors in this configuration:
How would you determine the probability of picking a marble of a specific color given these rules:
- 4 marbles are picked one after the other from the bag
- Once a marble is picked, all remaining marbles of the same color are removed from the bag
So as an example of how the process might happen:
- From the initial 20 marbles, the first one that is picked is blue
- All the remaining blue marbles are removed, leaving 12 marbles
- The next marble that is picked is black
- There aren't any black marbles left, so 11 marbles remain
- The next marble that is picked is red
- All the remaining red marbles are removed, leaving 5 marbles remaining
- The last marble that is picked is white
So a blue, black, red and white marble was picked, and only the green marbles remained untouched.
In essence the question is given the initial configuration and the rules, what are the probabilities for each of the colors of being picked. So the probability of 1 of the 4 marbles being Blue is x and the probability of 1 of the 4 marbles being Red is y.