Wiki Page, Statistics: Spring 2022: Lecture 12 (April 11 & 12)

Wiki Page
2023-04-11T09:42:43-06:00

Bell Work: Take notes on the lecture today and submit at least 5 key points as your bell work for each day.

3.1

Sample Space {S}: the set of all possible outcomes of an experiment.

Events: Subsets of sample space

Probability P(event): A number between 0 and 1 that reflects chance or odds of an event of a sample space occurring.

Example: Flipping a coin

Experiment: Flipping a coin

Sample Space = {Heads; Tails}

Event 1: Heads

Event 2: Tails

Probability P(Heads) = 0.5

Calculation =

number of chances for Heads = 1

number of total events = 2

P(Heads) = 1/2 = 0.5

Complement all outcomes that do not contain the outcome of the denoted probability.

Denoted by P(event)'

Example:

Experiment: Rolling a dice

S {1; 2; 3; 4; 5; 6}

Event: rolling a 3

P(3) = 1/total number of events = 1/6

P(3)' = 1 - P(3) = 1 - (1/6) = 5/6

Note: P(event) + P(event)' will always equal 1

Conditional probability: the probability that compares two events A and B where one event HAS already occurred to find the probability of the second event also occurring.

Denoted by P(A B): The Probability of B occurring "given" that A has already occurred.

P(A B) = P(A and B)/P(B) **P(B) must be > 0.

NOTE: Events can have multiple outcomes

3.2

Independent events: if an event in a sample space has no affect on other events occurring.

Dependent: if an event in a sample space does have an affect on the occurrence of another event in the sample space.

Example (independent): Choosing to go to school; Eating dessert.

Example (dependent): Getting in a car accident; Driving recklessly

Sampling with replacement: replacing an event to the sample space after it is picked. Therefore, a single event can be chosen more than once and the sample space does not change. Events here are independent.

Sampling without replacement: each member of a population may only be chosen one time. The events here are NOT independent.

Example (sampling with replacement): Rolling a dice two times in a row

Example (sampling without replacement): Choosing from a deck of cards and replacing the card after your first selection.

Mutually exclusive: two events do not share outcomes.

Example: Rolling a dice; Flipping a coin

NOTE: EVENTS CAN BE DEPENDENT/INDEPENDENT AND/OR MUTUALLY EXCLUSIVE/NOT MUTUALLY EXCLUSIVE.

3.3

Multiplication Rule & Addition Rule

Used for P(A and B)

Used for P(A or B)

NOTE: Be sure to define if the events share outcomes, and if the events are replaced, and if the events are mutually exclusive.

Exit Ticket (April 11)

1. Which two probabilities of an experiment will always sum to 1?

2. E and F are mutually exclusive. P(E) = 0.4; P(F) = 0.5. Find P(E F).

3. What does P(E or M) mean in words?

4. What does P(E F) mean in words?

Exit Ticket(April 12)

1.

2.