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POL 199
Basic Rules of Probability
Definitions
1. Random:
a. Doing something at random means that all the outcomes have an equal chance of
being the outcome.
2. Conditional Probability:
a. A conditional probability is one in which there is a restriction on something
happening first (for example, what is the probability that the second card drawn
from a deck of cards is a queen of hearts, given that the first card is not a queen of
hearts?.
b. This is written as
P(2nd card is queen of hearts | 1st card is not queen of hearts).
The vertical line is read as "given that".
3. Independence
a. Two things are independent if the chances for the second given the first are the
same, no matter how the first one turns out.
b. Otherwise, the two things are dependent.
c. (Drawing at random with replacement means that the draws are independent.
Drawing without replacement means that the draws are dependent).
4. Mutually Exclusive
a. Two things are mutually exclusive when the occurrence of one prevents the
occurrence of the other: in other words, one excludes the other.
5. What is the difference between mutually exclusive and independent?
a. Two events are mutually exclusive if the occurrence of one prevents the other
from happening.
b. Two events are independent if the occurrence of one does not change the chances
for the other.
Rules of Probability
1. Multiplication Rule
a. The chance that two things will both happen equals the chance that the first will
happen, multiplied by the chance that the second will happen, given that the first
has happened.
b. If two things are independent, the chance that both will happen is the product of
their unconditional probabilities.
2. Addition Rule:
a. To find the chance that at least one of two things will happen, check to see if they
are mutually exclusive. If they are, then you add the chances.
3. When do I add and when do I multiply?
a. Addition
i. The addition rule finds the chance that at least one of two things will
happen. (either A or B).
ii. Adding the probabilities requires them to be mutually exclusive.
b. Multiplication
iii. The multiplication rule finds the chance that two things will both happen.
(both A and B)
iv. Multiplying the unconditional probabilities of two events requires them to
be independent.