Theoretical+probability

toc =ACOS Objective 14=


 * Determine the theoretical probability of an event.**
 * Calculating the probability of complementary events and mutually exclusive events
 * Comparing experimental and theoretical probability
 * Computing the probability of two independent events and two dependent events
 * Determining the probability of an event through simulation
 * Example: using random numbers to find the probability of a basketball player making six baskets in six attempts if he makes 60 percent of his shots from the court and shoots 20 times during a game

ARMT Possible Points = 4 (MC, GR)
 * Both "and" and "or" situations may be included.
 * Fraction and percent may be used.
 * Word problems/real-life situations may be used.

Sample problems from Item Specs

=Definitions=


 * Complementary Events** - Events whose probabilities add up to 1 . Two events are complementary when one event occurs if and only if the other does not.
 * Flipping a coin: The two possible outcomes are heads or tails. The probability of heads (1/2) and the probability of tails (1/2) adds up to 1.
 * Drawing a marble out of a bag


 * Mutually Exclusive Events** - Two events that have no outcomes in common.
 * Being an 8th grader and being a member of the football team are not mutually exclusive. One person could belong to both.
 * Being an 8th grader and being a 7th grader are mutually exclusive. One person cannot be in both grades.

=Engages=

=Resources=
 * Play SKUNK
 * Ask likely/equally likely questions from How Likely Is It 1.2 or What Do You Expect 1.ACE.
 * Play the game Clue
 * Deal or No Deal
 * Show basketball clip of someone about to shoot a free throw (Hoop Dreams)
 * Simulation
 * Play Match/No-match, Making Purple, What's in the Bucket
 * What Do You Expect True/False quiz, lesson 7.2 (old book)

The AMSTI units What Do You Expect and __Clever Counting__ are great resources for teaching this objective.

Webquest: [|Step Right Up and Win a Prize]

What are my chances of winning? You probably ask yourself that question any time you play a game that offers a prize for winning. You're about to embark on a gaming adventure. You'll investigate the mathematical probabilities of winning various carnival games. You'll also research and design a game of your own. So, come on and take a chance! Sharpen up that hand-eye-coordination and grab your probability tool kit. This adventure is a win-win situation!

//Game Challenge 1:// Using the given carnival games and their data, complete different probability calculations and make predictions based on your calculated probabilities. //Game Challenge 2:// Second, research other carnival games and design a carnival game of your own. Then, prepare a report detailing why your game would be good to include in a school carnival. //Game Challenge 3:// Third, create presentation of your findings that includes a scale model or scale drawing(s) of your game.


 * Math Content:** compound probability, theoretical probability, experimental probability, simulations, scale drawing or model


 * Interdisciplinary:** Language arts (persuasive writing)

=Cool Problems=

If you roll two number cubes, what number is most likely to come up? Answer: //The Daily Spark Critical Thinking//, p. 25.
 * A Throw of the Dice**

It's time to get up. You roll out of bed, eyes still closed, and stagger over to your sock drawer. You know that you have three green socks, five red socks, eight blue socks, nine black socks, and twelve white socks scattered at random in the drawer. How many socks will you need to withdraw (keeping your eyes closed) in order to be sure you've got a matching pair? Answer: //The Daily Spark Critical Thinking//, p. 27.
 * Drawing Socks**

You have flipped a perfectly normal coin ten times and gotten heads every time. What is the probability that you will get heads the next time you flip it? Answer: //The Daily Spark Critical Thinking//, p. 36.
 * Flip a Coin**

=Video=

[| The High Stakes World of Statistics] This 26 minute video from [|United Streaming] (requires membership) contains 8 segments. They are targeted to grades 9-12, but some segments would be suitable for middle school. What's the chance you'll draw a face card out of a 52-card deck? That's one of many questions related to probability! Find out about probability and more. © 2002 Standard Deviants
 * Description:**

=Links=

My Filamentality [|Hotlist]

[|Determining Simple Probability] From AAA math...Explanation and practice with feedback, timed games

[|Fundamental Counting Principle] More from AAA

[|Majority Vote] What percentage does it take to win a vote? [|Matching Birthdays] In any group of six people, what is the probability that everyone was born in different months? [|Bones] Does drinking soda affect your health? [|Two Points] Probability question about basketball free throws [|I Win!] Is this game fair? [|Capture-Recapture] How many fish in the pond? [|Mis-Addressed] How could I send the check and not pay the bill?
 * Probability Problems from [|Figure This Math Challenge]**

[|National Library of Virtual Manipulatives Probability Activities] Coin toss, spinners, stick or switch, and more

[|Shodor Interactivate: Marbles] This activity allows the user to pull marbles from a 'bag' in a variety of ways in order to explore several different concepts involving randomness and probability. The user controls the number and color of marbles located in the "bag". The user can also change whether the marbles are replaced after each draw and if the order in which the marbles are drawn matters. A table presents the user with a summary of the trials, and allows them to explore the difference between experimental and theoretical results.