Two events are said to be independent if the result of the second event is not affected by the result of the first event.  If A and B are independent events, the probability of both events occurring is the product of the probabilities of the individual events. If A and B are independent events:

P(A and B) = P(A) • P(B)

Here is an example of independent event and how to calculate its probability:

A drawer contains 3 red paperclips, 4 green paperclips, and 5 blue paperclips.  One paperclip is taken from the drawer and then replaced (put back into the drawer).  Another paperclip is taken from the drawer.  What is the probability that the first paperclip is red and the second paperclip is blue?

Because the first paper clip is put back into the drawer, the sample space of 12 paperclips does not change from the first event to the second event. The events are independent. Therefore:

P(red then blue) = P(red) • P(blue) = 3/12 • 5/12 = 15/144 = 5/48.

If the result of one event IS affected by the result of another event, the events are said to be dependent.

If A and B are dependent events, and A occurs first, then:

P(A and B) = P(A) • P(B, once A has occurred)

Or:

P(A and B) = P(A) • P(B|A)

Here is an example of dependent event and how to calculate its probability:

A drawer contains 3 red paperclips, 4 green paperclips, and 5 blue paperclips.  One paperclip is taken from the drawer and not put back into the drawer.  Another paperclip is taken from the drawer.  What is the probability that the first paperclip is red and the second paperclip is blue?

Because the first paper clip is not put back into the drawer, the sample space of 12 paperclips is reduced to 11 paperclips from the first event to the second event. The events are dependent. Therefore:

P(red then blue) = P(red) • P(blue) = 3/12 • 5/11 = 15/132 = 5/44.