What is Probability Study Guide: GED Math

Practice problems for these concepts can be found at:

Data Analysis, Statistics, and Probability Practice Problems: GED Math

What Is Probability?

Ratios and proportions are ways to compare statistics (see Chapter 8). Similarly, you see probabilities, or predictions, all the time. Listening to the weather report, you may hear that there is a 30% chance of rain tomorrow. At judo class, you may hear that 11 out of 20 advanced students will attain a brown belt. On television, you might hear that four out of five dentists recommend a certain toothbrush. These are all ways to express probability. In this section, you will also learn what probability is and how to calculate it.

Probability is the mathematics of chance. It is a way of calculating how likely it is that something will happen. It's expressed as the following ratio:

The term favorable outcomes refers to the events you want to occur. Total outcomes refers to all the possible events that could occur.

A probability of zero (0) means that the event cannot occur. A probability of 50% is said to be random or chance. A probability of 100% or 1.00 means the event is certain to occur.

Probabilities can be written in different ways:

• as a ratio: 1 out of 2 or (1:2)
• as a fraction:
• as a percent: 50%
• as a decimal: 0.5

Example

Aili has four tickets to the school carnival raffle.

If 150 were sold, what is the probability that one of Aili's tickets will be drawn?

Plug the numbers into the probability equation:

P (winning ticket) =

Solve the equation.

There are several ways to write your answer.

Here are two of the ways. You can write the answer as a fraction: , which reduces to . Or you can write it as a percent: 2.7% (we rounded this answer up from 2.66666…).

Now let's look at problems that involve more than one event. Sometimes, the events are independent. That is, the first event does not affect the probability of events that come after it.

Example

You toss a penny and a dime into the air. What is the probability that both coins will land heads up?

You could list all the possible outcomes in a table like this:

Then, you could use this information to fill in the probability equation:

From the table, you know that there are four possible outcomes. Only one of those outcomes is heads/heads.

P (heads/heads) =

The probability of both coins landing heads up is , or 25%.

In this problem, you had very few possible events to list. In other problems, however, you might have many possible events to account for. Another way to solve this problem is by following these steps:

Step 1   Determine the probability that each event will occur.

Step 2   Multiply the probabilities together. The product is the probability that both of the two events will occur.

Sometimes the first event does affect the probability of the next event. In this case, the events are said to be dependent.

Example

A sack holds three purple buttons, two orange buttons, and five green buttons. What is the probability of drawing one purple button out of the sack and then—without replacing the first button—drawing a second purple button out of the sack?

Determine the probability that each event will occur. First, notice that the first event—drawing a purple button out of the sack—affects the probability of the second event because it changes both the number of purple buttons still in the sack and the total number of buttons in the sack.

The probability of drawing the first purple button is .

The probability of drawing a second purple button .

Multiply the probabilities together. The product is the probability that the two events will occur together.

The answer is , or 6.7%.

Practice problems for these concepts can be found at:

Data Analysis, Statistics, and Probability Practice Problems: GED Math