Discuss with your neighbor…Discuss with your neighbor…

What do you know about probability??

What are some real life examples that use probability?

Coin flip in sportsSpinners and dice in board games

Odds of survival in medical situationsInsurance

Predicting the weatherGuessing on a multiple choice tests

Gambling

ProbabilityProbabilityEQ: How do you calculate theEQ: How do you calculate the probability of an outcome?probability of an outcome?

Definition:Definition:

Probability is a number Probability is a number between 0 and 1 (or 0% between 0 and 1 (or 0%

and 100%) that describes and 100%) that describes how likely an event is to how likely an event is to

occur.occur.

To find probability:To find probability:

Make a fraction:Make a fraction:What you want on top and What you want on top and total things that could happen on bottomtotal things that could happen on bottomEx: What is the probability of getting heads Ex: What is the probability of getting heads

when you flip a coin? when you flip a coin? 1 on top (what you want can happen once)1 on top (what you want can happen once)2 on bottom (it could be heads or tails)2 on bottom (it could be heads or tails)

P(heads) = ½ P(heads) = ½

Try it:Try it:What is the probability of What is the probability of

getting a 2 when you roll a die?getting a 2 when you roll a die?1/6 1/6

What is the probability of What is the probability of getting an odd number?getting an odd number?

3/6 = ½ 3/6 = ½

CertainCertain vs. vs. ImpossibleImpossible

If something is If something is certaincertain, what , what does that mean?does that mean?

If something is If something is impossibleimpossible, , what does that mean?what does that mean?

Think about it:Think about it:

1.1. Name something that is Name something that is impossible.impossible.

2.2. Name something that is Name something that is certain.certain.

Discuss with a partner:Discuss with a partner:

1.1. What is a tree diagram?What is a tree diagram?2.2. Talk about how to make one for Talk about how to make one for

this situation: this situation: Dan is buying 2 snacks. He can Dan is buying 2 snacks. He can

choose from 3 different candy choose from 3 different candy bars and 4 types of chips. bars and 4 types of chips.

The ProblemThe ProblemYou need to buy a shirt and tie for a special

occasion. Your choices are shown below.

Use a tree diagram to find how many combinations of a shirt and tie are possible.

off-white white Solid blue Blue with pin stripes

White with pin stripes

navy blue yellow

Use a Tree Diagram to SolveUse a Tree Diagram to Solve

OWOW WW SBSB BPBP WPWP

NNBBYY NN BB YY NN BBYY NN BBYY NN BB YY

What is the probability of What is the probability of choosing a solid white shirt choosing a solid white shirt

and blue tie? and blue tie? OWOW WW SBSB BPBP WPWP

NNBBYY NN BB YY NN BBYY NN BBYY NN BB YY

P(SW & B) = 1 out of 15 or… 1/15

Another way to findAnother way to find the number of combinations… the number of combinations…

THE COUNTING PRINCIPLE!!

The Counting PrincipleThe Counting PrincipleYou can count the 3 ties for each shirt (5 shirts total)

OR…

You can multiply:5 shirts • 3 ties

=15 combinations!

Use the counting principle…Use the counting principle…

Mrs. Spanier flips a coin and then rolls a die. How many possible combinations can occur?

12

Now Mrs. Spanier flips a coin, and then ANOTHER coin, and then rolls a die. How many possible combinations can occur?

24

ONE ONE more way to find the possible more way to find the possible outcomes of multiple events…outcomes of multiple events…

A systematic or organized list!!!

Like a tree diagram without the branches.You can abbreviate and use a key.

Mrs. Miller flips a coin two times, Mrs. Miller flips a coin two times, and then rolls a die. How many and then rolls a die. How many possible combinations can occur?possible combinations can occur?

If you start with heads, and then heads…

Make a list for what you can then spin.

Now list heads then tails:Now list heads then tails:

Let’s Practice!Let’s Practice!

Use the COUNTING principle to find the possible number of combinations…

You are going to get an ice cream cone. There are 6 flavors of ice cream and 3 different cones.

You are buying a car. There are 2 body styles, 5 colors, and 3 models to choose from.

Use a TREE DIAGRAM to find the possible number of combinations:

You are picking out an outfit. You have 3 shirts (red, orange, and yellow) and 4 different pants (jeans, sweats,

shorts, dressy) to choose from.

What is probability that if I pick a person at random from this classroom, that I will pick:

A boy?

Someone with shorts on?

An alien?