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The Fundamental Counting Principal - PowerPoint PPT Presentation

Tree diagram Outcomes Sample space Event Fundamental Counting Principal Vocabulary Answer: The probability of the family having two girls is

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Outcomes

Sample space

Event

Fundamental Counting Principal

Vocabulary

Answer: The probability of the family having two girls is

CHILDRENA 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 four equally-likely outcomes with one showing two girls.

COINSA 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.

ICE CREAMAn 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.

Answer: There are nine different sundaes possible.

ICE CREAMAn 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?

Make a tree diagram to show the sample space. Then, find the probability that the sundae has vanilla ice cream.

Answer: So, the probability that a sundae chosen at random has vanilla ice cream is

• If you have 2 events: 1 event can occur m ways and another event can occur n ways, then the number of ways that both can occur is m*n

• Event 1 = 4 types of meats

• Event 2 = 3 types of bread

• How many diff types of sandwiches can you make?

• 4*3 = 12

CLOTHINGThe table below shows the shirts, shorts, and shoes in Gerry’s wardrobe. How many possible outfits can he choose consisting of one shirt, one pair of shorts, and one pair of shoes?

total number of outfits

numberof shirts

numberof shorts

numberof shoes

4

3

2

24

Example 3-1b

CheckYou can check your work by drawing a tree diagram and listing the 24 outcomes.

Answer: There are 24 possible outfits that Gerry can choose.

SANDWICHESThe table below shows the types of bread, types of cheese, and types of meat that are available to make a sandwich. How many possible sandwiches can be made by selecting one type of bread, one type of cheese, and one type of meat?

Outcomes

Sample space

Event

Fundamental Counting Principal

Things that could happen

List of all possible outcomes

A subset of the possible outcomes

If you have 2 events: 1 event can occur m ways

and another event can occur n ways, then the

number of ways that both can occur is m*n

11-23 odd

24-31 all