General Rules of Probability
General addition rule for any two events
For any two events A and B, P(A or B) = P(A) + P(B) - P(A and B)
Baye's rule
P(A|B) = P(B|A)P(A)/P(B)
When P(A) > 0, the conditional probability of B given A is
P(BIA) = P(A and B)/P(A)
Two events A and B are independent if
P(BIA) = P(B)
Bayesian statistics (Baye's rule)
Suppose B1, B2, .. Bn are disjoint events with positive probabilities, and the sum of these probabilities is 1.
Multiplication rule for any two events
The probability that two events A and B happen together can be found by: P (A and B) = P(A)P(BIA)
Two events are disjoint if
They can not occur at the same time (nothing in common), P(A and B) = 0
Tree diagram
A diagram used to show the total number of possible outcomes
Disjoint event
Events that have no outcomes in common
General addition rule for disjoint events
If A and B are disjoint events, P(A or B) = P(A) + P(B)
Disjoint vs independent
If A and B are disjoint, then the fact that A occurs tells us that B cannot occur - very dependent! Special multiplication rule holds if A and B are independent, but not otherwise
Multiplication rule for independent events
If two events A and B do not influence each other, the events are independent of each other. P(A and B) = P(A)P(B)
Two events are independent if
Knowing that one of the events has already occurred does not change the probability of the other event occurring.. P(AIB) = P(A)
Disjoint events are always associated with
The general addition rule of probability
Independent events are always associated with
The general multiplication rule of probability
Conditional probability
When we are trying to find the probability that one event will happen, given the info that the other event is already known to have occured