Investigation 4 Analyzing Compound Events Using Area Models Looking at two things happening and drawing an area model to help represent this data.

Homework Page 80 A 1,2,3,4,8, 13 B 5, 8, 13,15, 46 IXL DD4 and DD5

Vocab Expected Value The mean or average per turn of something happening, this number might not make sense to the problem, but remember it is an average What do you think the expected value would be for a game to be fai, like a carnival game Expected value should be zero

Investigation 4.1 Drawing Area Models to Find Sample Space How can an area model represent a situation to help analyze probabilities?

Area Models Event 1 would be on one side Write all the outcomes possible and draw a line across Event 2 would be on the top Write all the outcomes possible and draw a line down All the squares that are not inside the model represent all the possible outcomes that can happen, the sample space, some may look repeated but where you get the colored marble from matters. You can list outcomes and multiply the probability of each happening to get the value in the box What should all the boxes add up to?

Make an Area model for this situation

Another Area Model

Area Model vs Tree Diagram Could you make a tree diagram for each of the previous examples Each branch represents an event Tree Diagrams can get relatively big quickly

Investigation 4.2 Area Models and Probability How can you use experimental or theoretical probabilities of a compound event to predict the number of times one particular combination will occur out of any given number of repetitions of the event?

Make Purple Red plus Blue makes purple and purple wins Make an area model

Using your area model $72 8 people $48 $24

Investigation 4.3 Simulating a Probability Situation How is an area model for the one and one free throw situation like or unlike the area model for Making Purple game?

One-and-One Free Throw Nishi makes a free-throw an average of 60% of the time Free Throws in basketball are worth one point If you make the first shot you get to take a second shot What are the possible outcomes for this situation? Make an area model for this situation?   Make 60% Miss 40% Make both 36% Make first miss second 24% Miss first 40% Do no need Total = 100%

Investigation 4.4 Finding Expected Value How is the expected value different from probabilities of outcomes?

Expected Value This will help to determine if a game is fair Remember the average won or lost per turn If the school wants the game at the carnival they want to win more than lose, how would this be represented

One-and –One Expected value Nishi takes 100 shots How many times do you expect her to get 0 points? How many times do you expect her to get 1 point? How many times do you expect her to get 2 points? What is the total number of points she could score? Find the average number of points You just calculated the expected value

Calculating expected value Find probability of each situation Multiply each situation by the number of times they play Multiply each situation by the number of points Find the average Another way Find each persons probability Multiply each persons probability to the number of times they play Multiply answer from 2 to how much they make Subtract what the other person makes (this is what they pay out) Divide answer by number of times played to get the average

What does Expected Value tell us If only 2 people play one answer should be opposite each other, balance out to be zero A fair game would have an expected value of zero – this is the 2nd method