Sample Space Tree Diagram

What is the purpose of a tree diagram?

• To make the problem pretty.

• To show the total number of outcomes in a probability experiment.

• To find the area of the sample space in a probability experiment.

• To see if it is a experimental or a theoretical probability

What is a sample space?

• The answer to a probability problem.

• The area or perimeter of a probability.

• The total number of different results (or outcomes) you could get from an experiment.

• A probability that is always written as a percent.

You can make an outfit by picking 1 of 3 different shirts and match it with 1 of 2 different pants. What is size of the sample space?

• 6 Different Outfits (Black shirt, Black Pants) (Black Shirt, Jeans) (Brown Shirt, Black Pants) (Brown Shirt, Jeans) (White Shirt, Black Pants) (White Shirt, Jeans)

• 2 Different Outfits (Shirt, Black Pants) (Shirt, Jeans)

• 3 Different Outfits (Black Shirt, Pants) (Brown Shirt, Pants) (White Shirt, Pants)

• 1 Outfit (Shirt, Pants)

Use the tree chart to find the probability of randomly picking an outfit with a white shirt and jeans.

• There are 6 outfits

• 2/6, or 2 out of the 6 outfits have a white shirt with jeans

• 3/6, or 3 out of the 6 outfits have a white shirt with jeans

• 1/6, or 1 out of the 6 outfits has a white shirt with jeans.

For breakfast, you can choose to eat cereal or a bagel and to drink coffee, OJ, tea, or water. What is the sample space of this situation?

• 2, because there are 2 things to choose from to eat.

• 4, because there are 4 things to choose from to drink

• 10, because I see 10 different words on the tree diagram

• 8, because there are 8 different outcomes (cereal, coffee) (cereal, OJ) (cereal, tea) (cereal, water) (bagel, coffee) (bagel, OJ) (bagel, tea) (bagel, water)

What is the probability of randomly choosing a breakfast with a bagel and coffee?

• 1/8 because there is only 1 outcome out of the 8 possible choices that include both a bagel and coffee.

• 1/2 because there is only cereal and a bagel to choose from

• 1/4 because there is only one out of the four choices that include coffee

• 3 because the words "coffee" and "bagel" are on the diagram a total of 3 times.

What is the probability of randomly picking a breakfast with cereal?

• 1/8 because I only see the word "cereal" on the diagram once.

• 4/8 or 1/2, because half of the options come with cereal.

• 5/8, because there is the 1 cereal and the 4 drinks that could come with it (4 + 1 = 5)

• 1/4, because there is the 1 cereal and the 4 drinks that could come with it.

What is the sample space if I have 3 choices to pick from for lunch (hot dog, burger, pizza) 3 choices to pick from for a drink (milk, water, soda) and 2 choices for dessert (ice cream, cake)

• 8

• 12

• 18

• 30

What is the probability of randomly picking a lunch with pizza, soda, and ice cream?

• 1/18

• 3/18 or 1/6

• 13/18

• 1/3

What's the probability of randomly picking a lunch with pizza?

• 1/18

• 1/3, or 6/18

• 1/6, or 3/18

• 1/9, or 2/18