**Probability: Compound Events**

Independent Events

Since the first sock was replaced, choosing a red sock on the first try (event) has

NO EFFECT

on the probability of choosing a black sock on the second try (event).

Therefore, these two events are INDEPENDENT.

Create a Tree Diagram

Diane has a spinner with 3 equal sections and a quarter. Create a tree diagram of possible outcomes for spinning the spinner and flipping the coin.

Tree Diagram

Let's Recap!

Simple probability is the probability of _________ specific event occurring.

Theoretical

probability is calculated using ____________________, while

experimental

probability is determined by _______________________________.

Quantitative

probability is ________________ and is written as a ___________.

Qualitative

probability is___________________ but not ______________________.

Sample Space Recap

Probability is the ____________ of how

___________ an event is to occur.

A ________ _________ represents all

possible ____________ for an event or set of events.

Sample Spaces

List Tree Diagram Table

Create a Table

Diane has a spinner with 3 equal sections and a die. Create a table of possible outcomes for spinning the spinner and rolling the die.

Table

How many possible outcomes are there?

Create a Tree Diagram

Kathy is buying pizza for dinner. She has the choice of thin or pan crust. She needs to make a choice between pepperoni, sausage, or ham for toppings. Draw a tree diagram to show all possible combinations of crust and toppings.

Tree

How many outcomes are possible?

Compound Events Example 1

In a shipment of 20 computers, 2 are defective. Two computers are randomly selected from the 20 and tested. What is the probability that both are defective if the first computer isn't replaced after being tested?

Compound Events Example 1

Create a Table

Suzanne has a number cube and a quarter. Create a table of all possible combinations of outcomes for rolling a number cube and flipping a coin.

Table

Create a List

Sara has a red and blue pair of jeans. She also has a green shirt, white shirt and yellow shirt in her closet. She can wear either the orange or pink hat with any of these outfits. Create a list of possible combinations of of jeans, shirt, and hat to wear.

List

How many outcomes are possible?

Now it's your Turn

With a partner or individually, complete the sample space practice.

How many outcomes are possible?

Compound Event

A

compound

event is when there are _______ _______ _____ _______ simple events occurring.

Compound events can be __________________ or ___________________ .

What is the probability of spinning red and rolling a 5?

What is the probability of spinning red and rolling a 5?

What is the probability of rolling a 5 then rolling an even number?

What is the probability of rolling a 5 then rolling an even number?

The picture above represents a dresser drawer of socks. What is the probability that you will randomly choose a red sock, replace it, and then randomly choose a black sock?

Independent Events

Two events, A and B, are ______________

if the outcome of the first event (A) does ______ ________________ the outcome of the second event (B).

P(A and B) = P(A) x P(B)

The picture above represents a dresser drawer of socks. What is the probability that you will randomly choose a red sock, not replace it, and then choose a white sock?

How is this example different than the last example?

Dependent Event

Since the first sock was

NOT

replaced, choosing a red sock on the first try has an

EFFECT

on the probability of choosing a white sock on the second try. Therefore, these events are

DEPENDENT

.

Dependent Events

Two events are ______________ if the outcome

of the first event (A)

does

_____________ the outcome of the second event (B).

If the first event had not occurred, the outcome of second event would be ____________.

P(A and B) = P(A) x P(B)

Your Turn

With a partner or individually, complete the Probability Loop.

Compound Events Example 2

Victor flips 3 fair coins. What is the probability that he will get heads on the first 2 flips and tails on the last flip?

Compound Events Example 2

{BGO, BGP, BWO, BWP, BYO, BYP, RGO, RGP, RWO, RWP, RYO, RYP}