# Predicting Possible Outcomes Worksheets

We use probability to determine the likelihood that an event will occur. These events can be simple such as picking a King out of a deck of cards. Since there 4 kings in a deck of 52 cards, we would calculate the probability of this event to be 7.7% (4 ÷ 52 = 0.077). While it is not an impossible event to occur, it is not exact a common event. There are also many more complex situations where you may want to predict picking two cards consecutively. That is where you need to begin to pay attention and analyze everything that is happening. When you remove the first card, there were 52 possibilities, but on the second draw there are only 51 possibilities. We will explore events like this in this section. It is crucial that every time something changes in the event tree that you account for it. These worksheets and lessons help students learn how to use statistics to predict the outcome of different events.

### Aligned Standard: HSS-IC.B.6

- Richard's Spinner Step-by-step Lesson- How many possible outcomes are there when you use two spinners?
- Guided Lesson - Picking odd numbered tennis balls, flipping coins, hanging ornaments, and shopping for baby bottles.
- Guided Lesson Explanation - Only the second one requires a tree diagram, the others are two-steps.
- Practice Worksheet - I tried to think up as many possible random scenarios as possible.
- Matching Worksheet - Find the matching probability and problem.
- Probability Mutually Exclusive Events Five Worksheet Pack - These outcomes depend on being together.
- Probability Problems Involving AND & OR Five Worksheet Pack - Ten pages of work for you here.
- Probability the Complement of an Event Five Worksheet Pack - Students often have trouble with this particular skill. I would give them this over several days.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

A review on the creation of tree diagrams might be in order for these sheets.

- Homework 1 - Make a tree diagram, then count the branches. The first event has 6 outcomes: 1, 2, 3, 4, 5, and 6. The second event has 2 outcomes: heads (H) and tails (T).
- Homework 2 - John has 7 cards. He picks one at random. What is the probability of picking an even card?
- Homework 3 - Make a tree diagram, and then count the branches.

### Practice Worksheets

I tried to gravitate the questions towards the use of problems we have seen on exams. They aren't too creative.

- Practice 1 - Grace plays a game. She rolls a die and spins the spinner below. How many outcomes are possible?
- Practice 2 - Jack is in a shop. He wants to purchase balls. But there are different sizes available. The numbers indicate the size.
- Practice 3 - What is the probability of picking an even flower?

### Math Skill Quizzes

The numbers of the items work as labels which actually covers 2 standards in 1 here.

- Quiz 1 - Fredric flips a 2 sided coin and chooses one chocolate. If there are 15 different chocolates then how many outcomes are possible?
- Quiz 2 - At a new year party, we play different games. One game asks us to pick a ball and then pick a chocolate inside the bag. There are 6 balls and 10 chocolate in each bag. How many choices are possible for the player?
- Quiz 3 - Cups with 6 different kinds of designs with 3 colors are in a closet. How many total outcomes are possible if you randomly reach in and grab a cup?

### Using Statistics to Predict the Outcome of an Event

Statistics are not only used for collecting data but for using data to better understand situations. Once we analyze the data it allows us to make somewhat accurate predictions. This area of math is called predicative analytics. It is a widely growing career field as businesses are realizing that the more metrics that they analyze about their business, the better decisions that they tend to make. This task is slowly being dealt out to machines in the form of artificial intelligence. Here we will discuss different ways of how statistics can be used to predict an outcome of the event.

Let's start with a basic example, i.e. of a coin toss. In the coin toss, the odds are 50/50. Which means that either it will be heads or tails. This is an easy example, and there are further examples where statistics are utilized to predict the outcome of any event. For instance, a student can say that the likelihood that the instructor will take an exam is about 90% (or 0.9) from a maximum of 100%. By these statistics, the likelihood is that the instructor will take an exam that is almost certain. However, if the student says that there is a 50% chance that the instructor will take an exam, then he has a 50/50 chance. Such that there is a chance that the instructor might not take the exam as well. This is often referred to as theoretical probability where we simple divide the positive outcome by the number of possible outcomes. We use that value to predict simple events. These are events that cannot be broken down further, such as rolling a die.

As we gain more experience with the situations that we come across, the better and more accurate our predictions. The more data that is available to describe the conditions of the event, the more accurate our predictions will be. This is why predicative analytics is all about gobbling up as much data that is available all the time.