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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 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 5 9 .

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