Independent Events

Definition

Two events are independent if the occurrence of one event has no effect on the probability the other event occurs.

When the occurence of one event DOES have an effect on the probability the other event occurs, the events are said to be dependent.

Example One

When a coin is flipped and die is tossed at the same time, what you get on the coin ("head" or "tail") has no effect on what you get on the die ("1", "2", "3", "4", "5" or "6").

Example Two

Flipping a coin and getting a "head" has no effect on whether you get a "head" or a "tail" on the next flip of the coin.

Example Three

In a bag containing two red marbles and three blue marbles, if you draw a red marble with replacement (you put the red marble back in the bag after it is drawn), the probability of getting a red marble on a subsequent draw is the same as it was on the first draw.