Unit 4 AP Statistics Midterm (Probability Section)

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random process

 generates outcomes purely by chance

• unpredictable in short-term but predictable in the long run

Probability

likelihood of an event to happen

• proportion of times an outcome would occur in the long run

Law of Large Numbers

more trials means proportion approaches true probability (more accurate)

Simulation

imitates random process such that simulated outcomes are consistent with real-world outcomes

probability model

description of a random process that includes a list of all possible outcomes & the probability for each outcome to determine theoretical probability

Sample Space

List of all outcomes

sum of all probabilities is 1 (or 100%), each probability is between 0 & 1 (or 0% & 100%)

Event

any collection of outcomes from a random process

P(A) = (number of outcomes in event A) / (total number of outcomes in sample space)

Complement

the probability that an event does not occur

P(A^C) = 1 – P(A)

Intersection

P(A and B) = A ∩ B (both A and B must be true)

joint probability

Union

P(A or B) = A ⋃ B (at least one–either A or B, or both–must be true)

Mutually Exclusive Events

 cannot occur simultaneously (no outcomes in common) (also known as disjoint)

• if P(A and B) = 0

Addition Rule

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

Non-mutually exclusive events

can occur simultaneously

General Addition Rule

 P(A or B) = P(A) + P(B) – P(A and B)

Conditional Probability

probability that an event happens given that another event is known to have happened: P(A | B)

Conditional Probability Formula

P(A ∩ B) / P(B)

Independent Events

 knowing whether or not one event has occurred does not change the probability that the other event will happen

Independent Events Formulas

P(A | B) = P(A | B^C) = P(A)  OR P(B | A) = P(B | A^C) = P(B)

finding intersection (general multiplication rule)

 P(A and B) = P(A ∩ B) = P(A) * P(B | A)

Multiplication rule for independent events:

P(A) * P(B)

Mutually Exclusive v Independent

Mutually exclusive are automatically NOT independent

(if one happens, the other is guaranteed not to happen)