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Finding probability of an event (Basic probability rules (Two events A and…
Finding probability of an event
Random experiment
is an experiment that produces an outcome that cannot be predicted in advance (hence the uncertainty)
The
sample space (S)
of the random experiment is a list of possible outcomes
Once we have defined a random experiment, we can talk about an
event
of interest, which is a statement about the nature of the outcome that we're actually going to get once the experiment is conducted
In the special situation where all the outcomes in S are
equally likely
, we can find the probability of any event A by dividing the number of outcomes in A by the number of outcomes in S
Basic probability rules
Rule 1:
For any event A, 0 <= P(A) <= 1
Rule 2:
P(S) = 1; that is, the sum of the probabilities of all possible outcomes is 1
Rule 3 (The Complement Rule):
P(not A) = 1 - P(A); that is, the probability that an event does not occur is 1 minus the probability that it does occur
The event "event A does not occur" is called "
the complement event of A
"
Two events that cannot occur at the same time are called
disjoint
or
mutually exclusive
Rule 4 (The Addition Rule for Disjoint Events):
If A and B are disjoint events, then P(A or B) = P(A) + P(B)
Two events A and B are said to be
independent
if the fact that one event has occurred
does not affect
the probability that the other event will occur. If whether or not one event occurs
does affect
the probability that the other event will occur, then the two events are said to be
dependent
.
Not disjoint
and
independent
Not disjoint
and
not independent
Disjoint
and
not independent
Rule 5 (The Multiplication Rule for Independent Events):
If A and B are two independent events, then P(A and B) = P(A) * P(B).
Rule 6 (The General Addition Rule):
For any 2 events A and B, P(A or B) = P(A) + P(B) - P(A and B).
Probability table
Two-way probability table