Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.

Objective

Use tree diagrams to count outcomes and find probabilities

Vocabulary

Fair game

A game in which players of equal skill have an equal chance of winning

Vocabulary

Tree diagram

A diagram used to show the total number of possible outcomes in a probability experiment

Vocabulary

Sample space

The set of all possible outcomes of a probability experiment

Example 1 Draw a Tree Diagram

Example 2 Find the Number of Outcomes

Example 3 Find Probability Using Tree Diagrams

Outcome

CHILDREN A family has two children. Draw a tree diagram to show the sample space of the children’s genders. Then determine the probability of the family having two girls.

There are 4 possible outcomes

There is only 1 possible chance of having 2 girls

Answer: P(2 girls) =

1/3

Outcome

COINS A game involves flipping two pennies. Draw a tree diagram to show the sample space of the results in terms of heads and tails. Then determine the probability of flipping one head and one tail.

Answer: P(one head, one tail) =

1/3

ICE CREAM An ice cream sundae at the Ice Cream Shoppe is made from one flavor of ice cream and one topping. For ice cream flavors, you can choose from chocolate, vanilla, and strawberry. For toppings, you can have hot fudge, butterscotch, or marshmallow. Find the number of different sundaes that are possible.

Make a tree diagram to show the sample space.

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Make 3 columns:

Ice Cream Topping Outcome

Answer: There are 9 different sundaes possible.There are 9 different sundaes possible.

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Identify ice cream types

CARS A new car can be ordered with exterior color choices of black, blue, red, and white, and interior color choices of tan, gray, and blue. Find the number of different cars that are possible.

Answer: 12 different cars possible

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ICE CREAM An ice cream sundae at the Ice Cream Shoppe is made from one flavor of ice cream and one topping. For ice cream flavors, you can choose from chocolate, vanilla, and strawberry. For toppings, you can have hot fudge, butterscotch, or marshmallow. If you are given a sundae at random from the Ice Cream Shoppe, what is the probability that it has vanilla ice cream?

Use the tree diagram made in Example 2 to help find the probability

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Write probability statement

P (vanilla ice cream) =

probability that it has vanilla ice cream

Number with vanilla ice creamTotal number of sundaes

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P (vanilla ice cream) = Number with vanilla ice creamTotal number of sundaes

P (vanilla ice cream) = 39

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P (vanilla ice cream) = Number with vanilla ice creamTotal number of sundaes

P (vanilla ice cream) = 39 Find the GCF = 3

Divide GCF into numerator and denominator

3 3

P (vanilla ice cream) = 13

Answer:

CARS A new car can be ordered with exterior color choices of black, blue, red, and white, and interior color choices of tan, gray, and blue. If you select a car at random, what is the probability that the exterior color is blue?

Answer: P(blue) =

*

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Assignment Lesson 9:2 Tree Diagrams 7 - 14 All