When the outcome of one event does not affect the outcome of a
second event, the events are independent. When the outcome of one event
does affect the outcome of the second event, the events are dependent. For example: A box contains 3 white, 2 green, and 4 blue marbles. One marble is taken from the box and is NOT replaced. If another marble is drawn from the box, what is the probability that the first marble is white and the second one is blue?
Because the first marble is NOT replaced, the sample space of the second event is changed. The sample space of the first event has 3 + 2 + 4 = 9 marbles, but the sample space of the second event now has 8 marbles because the events are dependent. P(white then blue) = P(white) x P(blue) = 3/9 x 4/8 = 12/72 = 3/27.
