AP Statistics Chapter 5 - Probability

probability model

If S is the sample space in a(n) , P (S)= 1.

Conditional Probability

and Independence Two events A and B are independent if the occurrence of one event does not change the probability that the other event will happen.

probability model

If S is the sample space in a(n) , P (S)= 1.

Conditional Probability

and Independence Two events A and B are independent if the occurrence of one event does not change the probability that the other event will happen.

Complement rule

: P (AC)= 1- P (A) Addition rule for mutually exclusive events: If A and B are mutually exclusive, P (A or B)= P (A) + P (B)

General Multiplication Rule

The The probability that events A and B both occur can be found using the general multiplication rule.

5.1

Randomness, Probability and Simulation Probability The probability of any outcome of a chance process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions

Performing of a Simulation

The 4-Step Process 1

State

Ask a question of interest about some chance process

Plan

Describe how to use a chance device to imitate one repetition of the process

Do

Perform many repetitions of the simulation

Conclude

Use the results of your simulation to answer the question of interest

5.2

Probability Rules Sample Space The sample space S of a chance process is the set of all possible outcomes

For example

When a fair 6-sided die is rolled, the Sample Space is S = {1, 2, 3, ,4,5, 6}

For example

For the probability model above we might define event A = die roll is odd

Also be familiar with the notation

𝑷(𝑨 ∪ 𝑩)

Alternate notation

𝑷(𝑨 ∩ 𝑩)

For example

Using a deck of playing cards and drawing a card at random, the events A = card is a King, and B = card is a Queen are mutually exclusive because a single card cannot be both a King and a Queen

General Addition Rule If A and B are any two events resulting from some chance process, then P(A or B) = P(A) + P(B)

P(A and B) Venn Diagrams and Probability The complement Ac contains exactly the outcomes that are not in A

5.3

Conditional Probability and Independence Conditional Probability The probability that one event happens given that another event is already known to have happened is called a conditional probability