You picked two marbles from a bag and record their color. How can you make your selections independent events? Dependent events?

Let's suppose the next case:

We have a bag, where there are 5 red marbles, and 5 blue marbles.

We have a total of 10 marbles.

Suppose that we pick a marble and we do not replace it, and suppose that the first one is a red marble.

Then now we have in the bag a total of 4 red marbles and 5 blue marbles.

Now let's find the probability of picking a blue marble, this will be equal to the quotient between the number of blue marbles (5) and the total number of marbles (9)

P = 5/9

Now, suppose that instead of a red marble in the first pick, we had a blue marble.

Then now we have 4 blue marbles and 5 red marbles in the bag.

Again, the probability of picking a blue marble will be equal to the quotient between the number of blue marbles (4) and total numbergof marbles (9)

P = 4/9

Then the first pick does affect the probabilities for the second pick, this means that if we do not replace the first marble we pick, then the events will be dependent.

Now, if we replaced the first marble we picked (we put it again in the bag) then the number of blue marbles and red marbles is always the same, then in this case bot events will be independent (the first event will not affect the second event)