AP Statistics Chapter 5 Review

What is probability?

The percentage of times an outcome would occur in a very long series of trials is between 0 and 1.

Note: Probability is not accurate in the short run.

What is a random process?

Outcomes that are determined purely by chance.

What is the Law of Large Numbers?

If we observe more and more trials of any random process, the proportion of times that a specific outcome occurs approaches its probability.

How do you interpret the Law of Large Numbers in CONTEXT?

In a long sequence of a randomly selected _____, the estimated proportion of them ___ is (probability)

Example: In a long sequence of a randomly selected Lakeview resident, the proportion of them being a Cubs fan is 44%.

What is a simulation?

Imitates a random process in a way that simulated outcomes are consistent with real-world outcomes.

How do you use a random didgets table?

Step 1 (State): State what you’re being asked. (Examples are below)
Step 2 (Plan): Select random integers 1-4 until 4 prizes are represented (and the amount of times it takes to get all 1, 2, 3, and 4).

What is a sample space?

The set of all possible outcomes of a chance process (always adds up to 1).

What is a probability model?

A chance process that consists of two parts: A sample space (s) and a probability for each outcome.

What is an event?

A collection of outcomes from a chance process. (EX: They pass their class)

What is a complement?

The other outcome of an event

EX: The event is they pass their class, the complement is that they don’t pass their class)

What does Mutually Exclusive mean (important).

Two events are mutually exclusive if they have no outcomes in common and can never occur together.

P(A & B) = 0

MEANS YOU CAN ADD THEM.

What is the complement rule?

P(A^c) = 1-P(A)

What is the General Addition Rule? (Give definition and actual rule)

If A and B are any two events resulting from some chance process.

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

What does an Intersection mean?

The intersection of events A and B (Denoted by upside-down U) refers to the occurrence of two events at the same time. MEANS “AND”// OVERLAP

What does Union Mean?

Union of events A and B (denoted by U) means all of the outcomes in A OR B OR both. MEANS TO COMBINE; THINK “and” “or”

What is Conditional Probability?

The probability that one event happens given the other event happening.

What is the conditional probability formula?

P(B|A) = P(B and A)/P(A)

What is the General Multiplication Rule?

If A and B are any two events resulting from some chance process, then:

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

What does Independent Mean?

If the occurrence of one event does not change the probability that the other event will happen. (EX: Coin flips)

What is the Independent Formula?

P(A|B) = P(A)

How do you know something is independent?

If P(A|B)=P(A)

What is the Multiplication Rule for Independent Events?

If A and B are independent events, then the probability that A and B both occur is:

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

OR

P(A and B and C…) = P(A)*P(B)*P(C)…

When are you allowed to use this: P(A and B) = P(A)*P(B)?

If they are independent.

When are you allowed to use this: P(A or B) = P(A U B) = P(A)+P(B)?

If they are mutually exclusive.

When using a random digits table with conditional probability, what do you ALWAYS have to say?

You have to say no repeats.

When simulating Independent events (allow/don’t allow) repeats…

allow

When simulating conditional events, (allow/don’t allow) repeats…

don’t allow

Whenever you are repeating a simulation given the probability of the same event….

use exponents.