12.4 Counting Outcomes and Theoretical Probability.

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Presentation transcript:

12.4 Counting Outcomes and Theoretical Probability

Theoretical Probability: Counting the outcomes that are likely

Sample Space A list of all possible outcomes Use a tree diagram to find sample space Then calculate probability

Use a tree diagram to show all the possible outcomes for boys and girls in a family of three. Understanding a Tree Diagram

Use a tree diagram to show all the possible outcomes for boys and girls in a family of three. Understanding a Tree Diagram

Use a tree diagram to show all the possible outcomes for boys and girls in a family of three. Understanding a Tree Diagram

Understanding Possible Outcomes BBB BBG BGB BGG GBB GBG GGB GGG

BBB BBG BGB BGG GBB GBG GGB GGG Understanding Possible Outcomes

BBB BBG BGB BGG GBB GBG GGB GGG Understanding Possible Outcomes

BBB BBG BGB BGG GBB GBG GGB GGG Understanding Possible Outcomes

Probability of Multiple Events - Tree Diagrams A nickel, dime, and quarter are tossed. Find the probability of the following. 1) P(Only one heads) 2) P(At least two heads) 3 8 NickelDimeQuarterOutcomes H T H H H H H T H T H H T T T H H T H T T T H T T T H T H T H T H T H T H T

1) P(Only one heads) 2) P(At least two heads) 3 8 NickelDimeQuarterOutcomes H T H H H H H T H T H H T T T H H T H T T T H T T T H T H T H T H T H T H T = Probability of Multiple Events - Tree Diagrams A nickel, dime, and quarter are tossed. Find the probability of the following.

If you have four shirts, six pairs of pants and eight pairs of socks. How many different outfits can you wear? Finding How Many Total Outcomes Multiply each number of choices to find out the total number of outcomes Also known as: Counting Principle

You are offered ice cream with your choice of waffle or sugar cone, an ice cream flavor of vanilla, chocolate, or strawberry, and one of two toppings: chocolate chips or sprinkles.

1. Make a tree diagram to list the ice cream possibilities. 3. List your possibilities. 2. How many different ice creams (total outcomes) are possible? Make sure your list of possibilities has the same amount as the total number of outcomes.

4. What is the probability that your ice cream is with a topping of chocolate chips on a waffle cone? Write your answer as a fraction, a decimal, and a percent.

Homework Page 629 (4-17) all