# Simple & Compound Event Probability: Lists & Models

Instructor: Rhonda Ferguson

Rhonda has taught Computer App., writing through the college level, and math. She has an EdS. degree in Instructional Leadership and is working on a doctorate degree.

In this lesson, you will learn about simple and compound probability through the use of theoretical probability examples. The examples will include models using dice, marbles, cards, spinners, and tiles.

## What is Probability?

Ever wonder what your chances are of winning the lottery? Determining the chances of an event happening is called probability. Probability is usually written as a fraction, decimal, or percent. There are different types of probability. First, we will go over simple probability. Once we have an understanding about simple probability, we will then go over compound probability.

### Simple Probability

Simple probability is simple! With simple probability, we want to find the chance of one single event occurring. When learning probability, we often use real-world items likes coins, dice, spinners, marbles, tiles, or cards.

#### Examples

Let's take a coin for example. When you write probability as a fraction, you want to put the number of occurrences of the favorable event (or the event you would like) as the numerator, and the total amount of outcomes as the denominator.

So, if you were asked what is the probability of flipping tails on a penny, you'd have to ask yourself two questions.

First, how many times does 'tails' occur on a penny (or, how many tails are there on a penny)?

The answer is 1. Tails only occurs 1 time on a penny (or only one side of a penny has tails).

So, 1 will be your numerator.

Second, how many total outcomes are there?

The answer is 2. If you flip a coin, there are only two outcomes. Heads or Tails.

So, your denominator will be 2.

Finally, you will write your fraction.

The probability of flipping tails on a penny is 1/2, or 0.5, or 50% (Dividing the numerator by the denominator shows you the decimal as a fraction. Multiplying a decimal times 100 gives you a percentage).

Let's try another one. What is the probability of rolling a number greater than 4 on a six-sided die numbered 1 through 6?

First, how many times do the favorable events occur?

The answer is 2. On a six sided die numbered 1 through 6, the numbers greater than 4 are the numbers 5 and 6. Therefore, the numerator will be 2.

Second, how many total outcomes are possible if you roll a six-sided die?

The answer is 6. With a six-sided die, you could roll a 1, 2, 3, 4, 5, or 6.

Finally, you will write your fraction.

That makes 2/6 (remember to simplify) or 1/3 as your fraction, 0.33 as your decimal, and 33.3% as your percent.

So remember, total amount of favorable events over the total amount of possible outcomes.

### Compound Probability

Compound probability is similar to simple probability. Compound probability is actually a combination of 2 or more simple events. A compound event would ask what is the probability of flipping tails on a coin AND rolling a number greater than 4 on a six-sided die. There are a number of ways to answer this.

First, you could use the mathematical calculations way. You could take the probability of both events separately, then multiply them together. You could also create a list , or you could use a model that would show all possible outcomes of the two events, and see the amount of the favorable event out of the total amount of possible outcomes.

#### Mathematical Calculations Example

So, with the first method, if we are trying to find the probability of two events occurring, such as flipping tails on a coin, and rolling a number greater than 4 on a die, we would get the following two simple probability answers:

Flipping tails on a coin will be ½

Rolling a number greater than 4 on a die would be 1/3.

Using mathematics, we could multiply ½ by 1/3 and get 1/6 as our probability of flipping tails on a penny and rolling number greater than 4 on a six-sided die.

#### List and Area Model Examples

Now, don't just take my word for it. Let's prove it.

If I list all of the total outcomes available, I know that I could have the following:

I could flip heads and roll 1 (H1), flip heads and roll 2 (H2)……

Let's do this a faster way.

H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, or T6.

#### Area Model Example

This can also be shown as a model in the form of an area model, as shown in the picture.

Of all the possible outcomes from my list and model, there are only 2 that have tails and numbers greater than 4. Those two are T5 and T6. They are circled on the tree diagram.

That would make your numerator 2.

My denominator would be 12, because there are 12 possible outcomes in all.

Therefore, my fraction would be 2/12, or 1/6 (when simplified), 0.16, or 16.7%

### Another example

Let's try another one. Look at the marbles and tiles shown here.

If the tiles were face down and you had to pick a tile, and the marbles were in the bag and you had to pick a marble from the bag, what is the probability of you picking an 'T' and a blue marble?

Remember, there are three ways that we have covered to attempt to solve compound probability problems.

You could use the mathematical way, create a list, or use a tree diagram as a model. All three methods work well, and there is no need to do all three. You have to determine which method you are most comfortable with.

Let's solve it the mathematical way.

How many T's are possible from the tiles? 3!

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