# Dependent Events

Two events are dependent if the outcome of the first event affects the outcome of the second event, so that the probability is changed.

Example :

Suppose we have $5$ blue marbles and $5$ red marbles in a bag.  We pull out one marble, which may be blue or red.  Now there are $9$ marbles left in the bag.  What is the probability that the second marble will be red?

It depends.  If the first marble was red, then the bag is left with $4$ red marbles out of $9$ so the probability of drawing a red marble on the second draw is $\frac{4}{9}$ .  But if the first marble we pull out of the draw is blue, then there are still $5$ red marbles in the bag and the probability of pulling a red marble out of the bag is $\frac{5}{9}$ .

The second draw is a dependent event.  It depends upon what happened in the first draw.