Investigation 3 Making decisions with Probability Using probability to help analyze games of chance.

Homework Page 60 A 4, 5, 7, 9, 10 B 6, 7, 11, 12, 43-45 pick one IXL DD1 and DD3

Vocab Simulation A model used to find the experimental probabilities when it is not possible to work with a real situation

Investigation 3.1 Designing a Spinner to Find Probabiliteis How do you determine probability using a spinner?

Which spinner gives Kalvin the best chance of going to bed at 11 Which spinner gives Kalvin the best chance of going to bed at 11? Explain They are all the same, not matter how you look at the split up of times they always equal 50/50

Notes: Using a spinner to make probabilities Spinner represents 360 degrees Each part fraction of 360, angles over 360 Look at half, quarter third otherwise they will have to give you more information Total of an outcome add up all parts of the spinner

Example What is the theoretical probability that it will land on each time? Explain Suppose you spin the spinner 64 times, how many times should it land on each time? Explain

Investigation 3.2 Analyzing Fairness When using a tool to simulate a fair game, what things must you consider?

Think of a method that would work to choose a student fairly, be able to explain your process and reasoning. What do you think it means to be fair?

Notes: Fairness Fairness Each outcome needs to be the same probability Coin good for 2 things but not necessarily more than that Spinner each part has same amount of circle Names in a hat, each written once Rolling a die if each person is represented by the same number

Example

Investigation 3.3 Analyzing a Game How does understanding probability help you design a winning strategy?

Playing a Game: Roller Derby Each Group has two teams of two Each team has different colored markers, place all 12 on the Derby board, any way you want to and you can put multiple markers on the same column Each team roll a die to see who goes first, highest number goes first Teams take turns rolling the dice, find the sum of the dice and if you have a marker at that location take one off, only take off marker if you are the team rolling First team to remove all markers wins

Playing the Game What are some things you noticed? Find all the possible pairs of numbers you can get from rolling two number cubes. Find the sum for each of these outcomes. Are all the sums equally likely? Which sum occurs the most often?

Notes Order does matter when thinking of all combinations, even though the sum is the same, 2 and 6, 6 and 2 This is where a table of data would be helpful, probability tree would be very large Makes lists of all outcomes

Investigation 3.4 Designing and Using a Simulation How can you design a simulation to determine probability?

Making a Simulation or Experiment Take handout from the front Using your experimental data What is the probability of winning? How many different combinations of 2 scratch off spots are there, use this to find the theoretical probability How much do you need to spend to get 100 prize cards? How many video games can you expect to win with 100 prize cards?