This page should be used as a quick reference guide for this unit. Some terminology and concepts presented here are covered in more detail on other pages. Refer back to these rules as needed.
Basic Probability Rules
1) Possible values for probabilities range from 0 to 1
0 = impossible event
1 = certain event
2) The sum of all the probabilities for all possible outcomes is equal to 1.
Note the connection to the complement rule.
3) Addition Rule - the probability that one or both events occur
mutually exclusive events: P(A or B) = P(A) + P(B)
not mutually exclusive events: P(A or B) = P(A) + P(B) - P(A and B)
4) Multiplication Rule - the probability that both events occur together
independent events: P(A and B) = P(A) * P(B)
P(A and B) = P(A) * P(B|A)
5) Conditional Probability - the probability of an event happening given that another event has already happened
P(A|B) = P(A and B) / P(B)
*Note the line | means "given" while the slash / means divide
Mutually Exclusive - this indicates that two events cannot happen at the same time.
For example, consider the following two events: A) rolling a 2 and B) rolling an odd number. Since 2 is an even number, it's not possible for me to roll a 2 and for that number to be odd. Therefore, these events are mutually exclusive.
Independent Events - the probability of one event does not change based on the outcome of the other event
Consider a basketball player shooting 2 free throws. If the player's probability of making the second shot changes based on whether or not they make the first shot, then these events are dependent. If the probability does not change, then they would be independent.