Investigation 2 Experimental and Theoretical Probability Apply experimental probability to what if situations

Homework Worksheet on probability Bookwork page 40 13 IXL: V1 and V2

Vocab Outcome similar idea to a trial, an individual result of an action or event, toss a coin heads or tails Theoretical Probability a probability calculated by examining possible outcomes rather than doing an experiment A Fair game a game where all players have an equal chance of winning Tree Diagram an illustration of all possible outcomes, shows the total sample space Sample Space set of possible outcomes in an event Event what you are looking at the probability of Compound Event Consisting of two events happenings, or multiple events

Investigation 2.1 Finding Theoretical probabilities How does experimental probability compare to theoretical probability for a given situation?

Theoretical Probability Notes P(event) = number of ways outcome can occur / sample space What you want to happen is the outcome Sample space are all the total outcomes that can happen

Example A bag of marbles contains 8 yellow, 2 red, and 10 green marbles. An experiment consists of selecting one marble at random from the bag. Find the theoretical probability of each outcome. Selecting a yellow marble Outcomes = 8 Total outcomes = 20 8/20 = 2/5 0r 40% Selecting a red

Investigation 2.2 Developing Models What are some properties of theoretical probabilities?

Example

Notes Probabilities of all outcomes in an event should add to 100% You do not need to know the total of an event to use probabilities Can a probability be over 1, not unless everything is that outcome

Investigation 2.3 Designing a Fair Game How can you decide whether a game is fair or not?

Notes Tree Diagram – think of a sideways tree and the branches are all the different paths you can take Each branch/path represents an outcome for that event Start with just flipping a coin Rolling a die Picking marbles For the game to be fair all outcomes should have the same chance Flipping a coin, rolling a die, where the marbles problems fair

Example Make a tree diagram for flipping 3 coins What is the sample space? How many possible outcomes are there? Are all outcomes equally likely? What is the probability the coins will match? What is the probability only 2 coins will match? If all three coins are tossed an you win if they match and your opponent wins if they all do not match, is this a fair game?

Investigation 2.4 Using Strategies How can you determine all of the probabilities for a compound event?

Compound Event Notes Probability of two or more things happening Picking two marbles Rolling a die and flipping a coin

Example Picking two marbles from two similar bags Make a probability tree for picking 2 marbles What is the probability of choosing both the same color?