Probability Flashcards
Probability
Equips people to forcast future events and circumvent them.
Probability Formula
States that the likelihood of an event occurring is equal to the ratio of the number of favorable outcomes to the total number of outcomes.
Probability of an event happening P(E) = (Number of favorable outcomes) / (Total number of possible outcomes)
Events
Occurrances like the number on the die, a card drawn at random, a person in a neighborhood owning a lexus.
Mutually Exclusive
Events that cannot occur simultaneously
𝑃(𝐴∪𝐵)=𝑃(𝐴)+𝑃(𝐵)
Totally Exclusive (AKA Collectively Exhaustive)
At least one of the events will occur
Sample Space
The set of all possible outcomes
Classical Approach
Probability of an event A, P(A) in n mutually exclusive, equally likely outcomes with k implying outcomes is k/n
P(A) = Totalnumberofpossibleoutcomes (k) / Numberoffavorableoutcomes (n)
Conditional Probability
The likelihood of an event depends on the occurrence or non-occurrence of related events.
Formula: Pr(A∣B) = P(AandB) / P(B)
Independent Events
The occurrence of one event does not affect the probability of the other.
Ex: Flipping a coin and rolling a die. The result of the coin flip does not affect the die roll.
Dependent Events
The occurrence of one event affects the probability of the other.
Ex: Drawing two cards from a deck without replacement. The outcome of te first draw affects the probability of the second draw.
Complement of and Event
The complement of an event A (A^c), is the set of outcomes that do not imply the event A.
Formula: P(notA)=1−P(A)
Example: If the probability of it raining today is 0.3, then the probability of it not raining is 1−0.3=0.7
Union of Events
The union of two events A and B is the event that either A or B or both occur.
Formula for Mutually Exclusive Events: P(A∪B)=P(A)+P(B)
Formula for Non-Mutually Exclusive Events: P(A∪B )= P(A)+P(B)−P(A∩B)
Intersection of Events
The intersection of events A and B is the event that both A and B occur.
Formula: P(A∩B)
