[am4show have='p156;p158' guest_error='guest_error_msg' user_error='user_error_msg' ]Probability is when we take our best guess at how likely something is to happen (or not happen) by comparing the ratios and using our math skills. Probability is expressed either as a percent (from 0% - 100%) or as a decimal number (from 0 to 1).
There are over 40 videos on this page, so please take your time when working through the content. Most students will cover all of the content in 4-8 weeks.
Probability is used everywhere! "There s a 55% chance of rain today" means that there is a 55% chance that at least 0.01 inch rain will fall somewhere within the forecasted area.
If the probability is zero, that means that the event will never happen, so it has a 0% chance of occurring. If the probability is 1, that means the event will always occur, so it has a 100% chance of occurring.
Math Class Sessions
These Math Classes will start you out on the right path as we explore the wild world of probability. After watching the math lessons, continue to practice the concepts using the Probability Lesson Packet, activities, games, projects word problems and have fun learning!
The probability of something happen is the total number of favorable outcomes divided by the total number of outcomes. Before we dive into an example, let's define something called the sample space. The sample space is the set of all possible outcomes.
For example, if you toss a coin, you can either get heads or tails. So the sample space is either heads (H) or tails (T), and we write it like this: {H, T}
If you toss two coins, there's now four possible outcomes since there are two coins involved, so the sample space is {HH, HT, TH, HH}.
If you want to know what the probability of getting at least one head when you flip two coins, we need to modify the sample space to only contain events that include heads, so it would only have three, not four: {HH, HT, TH}.
In order for the event to occur (getting at least one head when you flip two coins), we divide the reduced sample space (3) by the total number of possible outcomes (4), which is 3/4 = 0.75 which means there's a 75% chance of this event (getting at least one head) occurring.
Probability events can be dependent or independent. If one event occurring does not affect the other, then the events are independent, like rolling two dice. The number rolled one die is independent of the number rolled on the other die.
Events are dependent if they do affect each other. Your chances of getting a parking ticket increase if you park illegally. Your chances of doing well on a math test increase if you study for it.
The next two videos cover these two types of events in more detail. Let's get started!
We have covered a lot of content in our live class so far! Let's review the content to really make sure you have a good handle on these important probability topics. The next two videos are a review with extra examples for you to work through with the teacher.
Probability Packet: Sections 1-2
This session uses a packet of lessons that we will be working through in place of a workbook. In addition to the content in the packet, you'll find seven different activities, one quiz, one study guide and a test to complete at the end when you've completed all the content in the packet.
Math Activity: Task Cards
This is a review of the ideas behind probability in a simple and fun way!
Probability Packet: Sections 3-4
Let's work on the next two sections of the packet along with some fun activities. You only need to print out the activities you want to do, you already have the entire packet printed for all six sections.
Math Activity: Probability Party Stations
Set up this fun, interactive exploration of theoretical and experimental probability using eight different stations to adventure through!
Math Activity: Puzzle Train
This fun activity is part-scavenger hunt, part probability practice of making predictions. Let's use the math skills we've covered so far to work through these problems together!
Math Activity: Simple & Compound Events Mazes
Let's get lost in a maze while figuring out the probability of both simple and compound events.
Probability Packet Mid-Unit Quiz
After you've completed parts 1-8 (Student Handout & Homework Sections 1-4), it's time to review everything we've covered with a quiz. Use this quiz more as an assessment to make sure you've comfortable with everything we've covered so far. If you find you need more time with a particular area, go back to that section and review the material a little more.
Probability Packet: Sections 5 & 6
This is the last section of the Probability Packet that explores independent and dependent events. Make sure you've completed sections 1-4 above before starting on the second half of the packet. (Note: the PDF download included all six sections.)
Math Activity: He Said, She Said
Join me in figuring out who's right in this set of ten questions in this fun error analysis game.
Math Activity: Probability of Dependent Events
This is a fun way to practice word problems and probability using a cut and paste activity!
Probability Review: 28 Task Cards
After you've completed all of the Probability Packet (sections 1-6), it's time for a review activity! If you find you need more time with a particular area, go back to that section and review the material a little more.
Probability Packet: Study Guide & Unit Test
After you've completed all of the Probability Packet and all the activities (Student Handout & Homework Sections 1-6 and all seven activities), it's time to review everything we've covered with a study guide before taking the final test. Use this test more as an assessment to make sure you've comfortable with everything we've covered. If you find you need more time with a particular area, go back to that section and review the material a little more.
Probability of Unusual Dice
If you love using dice in games, then you'll enjoy these next set of videos, where we explore the special probability properties of three different sets of dice.
Probability Application
While it's fun to play games with probability, and in fact most math teachers will only have activities limited to dice, cards, spinners, and flipping coins. That's because in real-world applications, the level of complication is very high by the time probability is introduced as a method of solving complex problems.
Probability deals with figuring out how likely an event will happen in the future, based on mathematical models that we create that make use of knowing which factors will influence the likelihood of the event happening.
Statistics analyzes things that have already happened, like how much lemonade you sold, how long it took to get to work in rush hour, or how many students skip school close to a holiday.
Statistics and probability often work together, because the more you understand patterns about the situation and things that influence it, the better your prediction for the future will be. It's a lot easier to figure out how much inventory to buy for this year if you already have records of how many sales you made over the last few years. In the following mini math course on Statistics, we'll be making predictions to help businesses make important decisions that use both the statistics and probability math skills we've been learning.
Probability Science Project
Imagine you are an astronomer. You have scientific data on thousands of stars. You want to learn about what the universe is like without having to go out and measure every single star in the night sky (which you couldn't do anyway, there's just too many!), so instead, you take smaller samples and look them over, exploring and discovering patterns in your sample to help you make predictions about what you might find in the universe on a larger scale. Let's find out how to do this in this special lab that uses real scientific data!
Math Challenge
I have a special Math Challenge for you to work on after you work through some of the content in probability. Remember, the goal for these math challenges is for you to be able to communicate your great ideas with your family and friends, without them being in a math class or having any knowledge of a specific area of math. You should be able to convey math ideas to most people that are interested in hearing what you have to share.
We want you to learn how to not only communicate your great ideas but also be able to listen to others and understand their solutions as well, and perhaps you can all come to a newer, improved solution that no one had initially!
If you need a HINT... please look below the Math Challenge for my tips on how to think about the problem. That should get you started on the right track. Have fun!
Tips for the Math Challenge:
For the 3-Door Math Challenge, if we also consider the following three points, it makes it a lot more clear how to think about the problem. First, the host's action is dependent on the participant's selection. Think about these conditions:
- The host must always open a door that was not picked by the contestant.
- The host must always open a door to reveal an empty space and never the car.
- The host must always offer the chance to switch between the originally chosen door and the remaining closed door.
If you get stuck, try going at this problem backwards by mapping out each of the three cases, putting the car behind each door in turn and pretending to be the host. Which doors are you allowed to open, and how does that change when the participant randomly selects the door with the car?
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