# 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.

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