Conditional+Probability,+Orem+HS+Core+Academy,+June+2012

This an addendum to the core academy learning cycle to carry over into the honors standards.

Solidify the ideas of independent and disjoint events by adding the following:


 * Add one additional question to each page of the Representations of Categorical Data; "Are the events Mutually Exclusive?"
 * Add one additional page with data that is mutually exclusive and dependent, but intuitively it should be independent. Ex. Probability of dying in a plane crash and probability of dying in a car crash.

This is a Solidify/Practice Task Intuition is not always good enough. Conditional probabilities Independent and dependent events How math can help us make decisions. S.MD.7 (+) Analyze decisions and strategies using probability concepts
 * __Big Goal__**
 * 1) Prob(win| switch strategy)
 * 2) P(win| stay strategy)

- disjoint and mutually exclusive – defined it and discussed in Sally’s error - talked about dependent events in the Titanic exercises if survival was dependent on Gender or class [] This is the classic “Let’s Make a Deal” problem. There are two goats and one prize behind the curtains, choose a curtain number, Monte Hall shows you a goat, and asks if you want to keep your choice or switch.
 * __Pacing__**: Right after Titanic II or III when we discuss independent and dependent data
 * __Background knowledge__**
 * __Practice Standards__**
 * 1) Attend to precision
 * 2) Making sense and persevere
 * 3) Reason abstractly and quantitatively
 * 4) Look for and express regularity in repeated reasoning
 * 5) Model with mathematics
 * 6) Construct viable arguments
 * __Task and Justification of Placement__**

__Launch__ Pose the following situation to the students: During a certain game show, contestants are shown three closed doors. One of the doors has a big prize behind it, and the other two have junk behind them. The contestants are asked to pick a door, which remains closed to them. Then the game show host, Monty, opens one of the other two doors and reveals the contents to the contestant. Monty always chooses a door with a gag gift behind it. The contestants are then given the option to stick with their original choice or to switch to the other unopened door. In groups, students can discuss what they might do.

__Explore – anticipate student work __ The probability of winning once a door is shown is ½. Because it’s still 50-50, one door is a winner and one a loser. A Venn diagram (we’re not sure this would be successful) Two-way tables of choose and win or lose Strategies – stick or switch Acting it out with “doors” and “prizes” __Cognitive level__ – rather complex (3) __Posing the problem__ In small groups, discuss the following strategies. If you were the contestant, which of the following strategies would you choose, and why?

 Strategy 1 (stick): Stick with the original door

 Strategy 2 (flip): Flip a coin, stick if it shows heads, switch if it shows tails

 Strategy 3 (switch): Switch to the other door

Answer the following questions: - P(Win|stick strategy) - P(Lose|stick strategy) - P(Win|stay strategy) - P(Lose|stay strategy) - P(Win|flip strategy) - P(Lose|flip strategy) - [teacher note: These probabilities can lead to a discussion of complementary events or disjoint events] - Explain why or why not the winning and the stick strategy are independent? - Explain why or why not the winning and the flip strategy are independent? [teacher note: they are independent] - Explain why or why not the winning and the stay strategy are independent?

__Anticipated responses__ Tree diagrams Two-way tables