ACOS Objective 13

Determine the probability of a compound event.
ARMT Possible Points = 6 (MC, GR, OE)

  • The drawings of one or more spinners may be used.
  • Coins may be used.
  • Compound events with replacement or without replacement will be required.
  • Word problems/real-life situations may be used.

Sample problems from Item Specs


The AMSTI unit What Do You Expect is a great resource for teaching this objective.
The 8th grade unit Clever Counting has several activites appropriate for 7th grade.

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

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

Drawing Socks

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.

Flip a Coin

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.


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


Stick or Switch
In this TI-activity, students will simulate an experiment to determine the best strategy for winning a game, whether it is staying with the card originally picked or switching to the other card. Each strategy and outcome is given a number. The numbers will be collected in a list.

My Filamentality Hotlist

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

Fundamental Counting Principle
More from AAA

Probability Problems from Figure This Math Challenge
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?
Does drinking soda affect your health?
Two Points
Probability question about basketball free throws
I Win!
Is this game fair?
How many fish in the pond?
How could I send the check and not pay the bill?

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.