Probability in Geometry

Theoretical Probability

number of favorable outcomes/number of possible outcomes

Sample Space

List of all possible outcomes for an experiment. Use fundamental counting principle to find.

Fundamental Counting Principle

Used to find the number of events in the sample space for multiple-part events. Multiply the number of possible outcomes for each part together.

Independent Events

The outcome of one event does not affect the probability of the next event.

Dependent Events

The outcome of one event affects the probability of the next event.

Probability of Independent/Dependent Events

Multiply the probability of each event. (Coin flip and rolling even on a die would be (1/2)×(1/2)).

complement

Complement of an event is basically the opposite of the event being considered. (if event is heads on a coin, complement is tails

Notation of Complement

read as "A bar," capital A with line over it.

Experimental Probability

When we can’t compute a theoretical probability for an event, we can gather data and base the probability on what has happened in the past.

Disjoint/Mutually Exclusive Events

Events that have no common outcomes. In other words, both events cannot happen at the same time.

Overlapping Events

Events that have at least one common outcome. In other words, both events can happen at the same time.

How to find P(A or B) in a disjoint event.

P(A or B) = P(A) + P(B)

How to find P(A or B) in an overlapping event.

P(A or B) = P(A) + P(B) – P(A and B)