Discuss with your neighbor… What do you know about probability?? What are some real life examples that use probability?

Coin flip in sports Spinners and dice in board games Odds of survival in medical situations Insurance Predicting the weather Guessing on a multiple choice tests Gambling

EQ: How do you calculate the probability of an outcome?

Definition: Probability is a number between 0 and 1 (or 0% and 100%) that describes how likely an event is to occur.

Ex: What is the probability of getting heads when you flip a coin? To find probability: Make a fraction: What you want on top and total things that could happen on bottom Ex: What is the probability of getting heads when you flip a coin? 1 on top (what you want can happen once) 2 on bottom (it could be heads or tails) P(heads) = ½

Try it: What is the probability of getting a 2 when you roll a die? 1/6 What is the probability of getting an odd number? 3/6 = ½

If something is certain, what does that mean? Certain vs. Impossible If something is certain, what does that mean? If something is impossible, what does that mean?

Think about it: Name something that is impossible. Name something that is certain.

Discuss with a partner: What is a tree diagram? Talk about how to make one for this situation: Dan is buying 2 snacks. He can choose from 3 different candy bars and 4 types of chips.

The Problem You 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 Solve OW W SB BP WP N B Y N B Y N B Y N B Y N B Y There are 15 combinations!

What is the probability of choosing a solid white shirt and blue tie? OW W SB BP WP N B Y N B Y N B Y N B Y N B Y P(SW & B) = 1 out of 15 or… 1/15

Another way to find the number of combinations… THE COUNTING PRINCIPLE!!

The Counting Principle You 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… 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 more way to find the possible 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, and then rolls a die Mrs. Miller flips a coin two times, and then rolls a die. How many 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: H H 1 H T 1 H H 2 H T 2 H H 3 H T 3 H H 4 H T 4 H H 5 H T 5 H H 6 H T 6 Finish the list! Do you get 24 combinations?

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?