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). 

Example:
A drawer
contains 3 red paperclips, 4 green paperclips, and 5 blue
paperclips. One paperclip is taken from the drawer and then
replaced. 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 replaced, the sample space of 12 paperclips does
not change from the first event to the second event. The events are
independent.
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, the probability of both events occurring is
the product of the probability of the first event and the probability of
the second event once the first event has occurred.
If A
and B are dependent events,
and A occurs first,
P(A and B) = P(A) • P(B,once A has occurred)
... and is written as ...
P(A and B) = P(A) • P(BA) 


Example:
A drawer
contains 3 red paperclips, 4 green paperclips, and 5 blue
paperclips. One paperclip is taken from the drawer and is
NOT
replaced.
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 replaced, the sample space of the second event
is changed. The sample space of the first event is 12 paperclips,
but the sample space of the second event is now 11 paperclips. The
events are dependent.
P(red then blue) = P(red) • P(blue) = 3/12 • 5/11 = 15/132 = 5/44.


Don't
panic! You can do it!
Probability is mostly common sense. 

