Introduction/Small Review o Simple probability with a dice Show the probability of this independent event and the odds that you roll a certain number(s) on the die Probability you roll a “3” o 1/6 = 16.667% Probability you roll an “odd” number o Independent Event Elaborate on what independent means o Dependent Event (with bag of marbles) Show what happens when you do not replace the item after pulling it out, thus making it dependent 10 blue marbles, 5 red marbles, 5 green marbles. What is probability of selecting a blue marble then without replacing it select another blue marble. 10/20 x 9/19 = 23.68% Learning Objective o After completing this lesson, the student will be able to recognize the change in probability with the varying number of possibilities in the sample space. Launch o Start “Lets Make a Deal” Game Show Go to http://www.grand-illusions.com/simulator/montysim.htm show sample trial Put everyone in groups of four and show them how to play the game (3 groups) Have them record fifty trials per group Video of sample trial http://youtu.be/iqipbdkoM6w Student experiment o Keep them in groups for now Have them form predictions about trends and tendencies Expected Student Responses o “Switching is better” o “You are more likely to win if you switch” o “You have over a 50% chance to win if you switch.” o “You have less than 50% chance to win if you stay.” Have a class discussion about the predictions and write them down o Have the groups form together to make one big group Have them compile their results One group’s win probability might be higher than the theoretical probability and vice versa Go back to the predictions made and prove them either wrong or right Sum up their averages and interpret the information for them Formative Assessment Item o The final Monty Hall question (as class) Have the class answer one final Monte Hall problem. Ask the class to select a door. Reveal another door. Then ask the class if they want to switch or stay. Grand prize is candy (if lose still get candy) Prove (Technology) o Show that after many tries, the experimental probability will equal the theoretical probability o For this we will use technology to complete a large number of trials (e.g. 1000) to prove that using the law of big numbers the experimental probability will be the same as theoretical probability. Show them formula for n amount of doors o ((n - 1)/ n) x (1/(n-k-1)) Ask class what they think each variable stands for Possible student responses o “n/k is the total number of doors” o “n/k is the number of doors not opened up” n = number of total doors k = number of total doors opened o Show them how this formula works for any amount of doors Homework: #1) There are 5 doors with a prize behind only one of them. What is the probability you will win the prize if you pick a door and then 2 doors that don’t have the prize behind it are revealed and then you switch to a different door? A: 40% Chance #2) There are 1568 doors with a prize behind only one of them. What is the probability you will win the prize if you pick a door and then 938 doors that don’t have the prize behind it are revealed and then you switch to a different door? A: 0.159% Chance Process Standards PS.P.3: Understand the multiplication counting principle, permutations, and combinations; use them to solve real world problems. Use simulations with and without technology to solve counting and probability problems. PS.P.6: Analyze decisions and strategies using probability concepts. Analyze probabilities to interpret odds and risk of events. Common Core Standards CCSS.Math.Practice.MP2 Reason abstractly and quantitatively. CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.