AP Statistics Probability Rules Definitions n Probability of

AP Statistics Probability Rules

Definitions n Probability of an Outcome: A number that represents the likelihood of the occurrence of an outcome. n Alt. : The proportion of times the outcome would occur in a very long series of repetitions.

Definitions n Theoretical Probability: probability values arrived at through calculations. n Empirical Probability: probability values arrived at through observation or simulation.

Basic Rules for Probability All possible outcomes must have a combined probability of 1.

Basic Rules for Probability n P(A) = 0 if and only if A is certain not to occur (impossible event). n P(A) = 1 if and only if A is certain to occur. n The probability that event A will fail to occur is denoted P(Ac), or the complement of A. n P(Ac) = 1 – P(A).

The Complement Rule states that; P(A)+P(Ac)=1 § P(Sample Space) = 1, because the sample space represents all possible outcomes. Therefore: § P(A)+P(Ac) = P(S) = 1 § Either event A happens or it doesn’t happen. There are no other choices! § § “At Least One” Rule § P(At least one) = 1 – P(none)

Another Probability Rule: If A and B are disjoint (can’t happen at the same time), then: P(A or B) = P(A) + P(B) n This is the Addition Rule for Disjoint Events. n

Addition Rule n The word “or” means “addition” in the language of probability. n Note that P(A or B) can also be written as: and can be stated as “A union B”.

Example n For women age 25 to 29: Marital Status Probability Never Married. 353 Married Widowed. 574 . 002 Divorced. 071 P(never married or divorced) = P(never married) + P(Divorced) n =. 353 +. 071 =. 424 n

Independence n Definition: Two events are independent when knowing that one occurred does not change the probability that the other occurred. n Coin flips and dice rolls are independent.

Independence n If two events are independent, then the probability of both A and B occurring is: n P(A and B) = P(A)∙P(B) n This is the Multiplication Rule for Independent Events. n Example: we roll a die twice with P(even)=. 5 and P(odd) =. 5. n P(even and odd) = (. 5) =. 25

Multiplication Rule for Independent Events n The word “and” means “Multiplication” in the language of probability. n Note that P(A and B) can also be written as: and can be stated as “A intersect B”.

Example For Dependent Events

Homework n Worksheet.