Odds are, here is one topic you’ll probably see on GED Math: probability (see what I did there? 😉 ). Read on to learn all about probability and try your hand at a couple of questions that look like what you might see on the GED Mathematics test.

## What is Probability?

**Probability** is the likelihood of an event happening. Whether the event is cataclysmic, like an asteroid hitting the earth, or relatively tame, like rolling a six in a game of Yahtzee, you can calculate the likelihood of it happening, so long as you have enough information about variables and possible outcomes. Calculating the probability of an asteroid hitting the earth is a complex undertaking; however, calculating the probability of rolling a six is a rather simple process. We call it, in fact, simple probability.

## Simple Probability

**Simple probability** is the likelihood of a single event happening. Most of the probability questions you’ll see on the GED Math exam involve simple probability.

Simple probability is calculated by using a formula:

- A
**favorable outcome**is an event that goes the way you’re trying to predict. It is not necessarily a good event. For example, an asteroid hitting the earth would be “favorable” if you’re trying to calculate the odds of it happening. So would rolling a six. - A
**possible outcome**is any event that could happen, including the favorable one. These are all the things that*could*happen, whether they actually will or not.

For example: Say you really do want to roll a six in a game of Yahtzee. The only favorable outcome is rolling a six, so the number of favorable outcomes is 1:

What is the number of possible outcomes? Well, if you are only rolling one standard die one time, there are 6 possible outcomes. This is because there are 6 numbers on a die. You could roll a 1, 2, 3, 4, 5, or 6. That’s 6 possible outcomes:

1st possible outcome | Roll a 1 |

2nd possible outcome | Roll a 2 |

3rd possible outcome | Roll a 3 |

4th possible outcome | Roll a 4 |

5th possible outcome | Roll a 5 |

6th possible outcome | Roll a 6 |

You couldn’t roll a 0 or a 7. You also couldn’t roll any number more than once, since you are only throwing one die one time. So:

## Compound Probability

Finding out the probability of rolling a 6 with one die and one toss is easy enough, but say you want to try to roll a 6, and then on a second toss, you want to roll a 5. Now you have a compound event, because two events must happen in order for the outcome to be favorable:

Event: | Rolling a 5, then rolling a 6 |
---|---|

Event 1 | Roll a 5 |

Event 2 | Roll a 6 |

- Note that you do not have two favorable outcomes, because you must roll a 6 and a 5, in this order. Both of these things must happen in order for the outcome to be favorable. Both things happening together equal a single favorable outcome for the probability of the combined event.
- Also note that rolling a 6 on the first toss does not change the likelihood of rolling a 5 with the second toss. Since the probability of one thing happening does not affect the likelihood of the other thing happening, the two events are said to be
**independent**. There is such a thing a dependent event, where the outcome of one event*does*affect another event, but you don’t have to worry about that for the GED. Only independent events will show up on the GED Math exam.

The probability of multiple events both happening is called **compound probability**, and it involves finding the likelihood of two or more independent events happening together.

### Calculating Compound Probability

To calculate compound probability, you first need to calculate the simple probability of each event happening separately.

We already found out that the probability of rolling a 6 is ^{1}⁄_{6}. What is the probability of rolling a 5? Well, even though it is a different number, the probability is the same, since the die still has six sides, and there is only one 5 on the die.

1st possible outcome | Roll a 1 |

2nd possible outcome | Roll a 2 |

3rd possible outcome | Roll a 3 |

4th possible outcome | Roll a 4 |

5th possible outcome | Roll a 5 |

6th possible outcome | Roll a 6 |

So, the probability of rolling a 5 is also 1 out of 6, or ^{1}⁄_{6}.

To calculate compound probability, multiply the simple probability of the two independent events happening:

Remember that to multiply two fractions, you multiply across: first multiply the numerators together, then multiply the denominators together. As with regular fractions, you should simplify the product, if possible.

For example, the probability of rolling a 6 is ^{1}⁄_{6}, so:

The probability of rolling a 5 is also ^{1}⁄_{6}, so:

So, the probability of rolling a 6 and then a 5 is 1 out of 36, or ^{1}⁄_{36}.

## Expressing Probability

There are three common ways to express probability: as a fraction, decimal, or percent. You may see any one of these used on the GED Math exam. You may also see probabilities written out as words (e.g., “1 out of 6”).

### Fraction

We have already shown a common way to express probability, and that’s in the form of a fraction. If the probability of rolling a 6 with 1 die is ^{1}⁄_{6}, you would say “one out of six.”

### Decimal

If the likelihood of an event is 1 out of 6, to find the decimal, you would convert the fraction just as you would any other fraction; that is, by dividing the numerator by the denominator.

Remember:

- The numerator is the number above the fraction bar.
- The denominator is the number below the fraction bar.

For example, ^{1}⁄_{6}=1÷6=0.1667. So, you could also say that the probability of rolling a 6 with 1 die is about 167 thousandths.

### Percent

To express the probability as a percent, convert the decimal to a percent, just as you would any other percent: by looking at the hundredths place.

- Remember that a percent is a value out of 100. So to find a percentage from a decimal, you are looking for how many hundredths the decimal shows.
- The hundredths place is the digit two places to the right of the decimal point.
- It is okay to round up or down if your decimal expands for many place values.

For example, the decimal 0.1667 can be rounded to 0.17. This is 17 hundredths, or ^{17}⁄_{100}, which equals 17 percent. So, there is about a 17% chance that you will roll a 6 with 1 die.

## GED Math: Probability Sample Problems

Ready to practice with simple and compound probability>? Try these sample problems.

1. Billy has a bag full of candy. The bag has 6 strawberry candies, 3 watermelon candies, and 4 green apple candies. What is the probability of Billy randomly pulling a green apple candy from the bag?

a.) 1 out of 4

b.) 1 out of 14

c.) 4 out of 4

d.) 4 out of 13

2. Amanda tosses a quarter 4 times. She wants to toss a heads, then a heads, then a tails, then a heads. What is the likelihood of this happening?

a.) 1 out of 16

b.) 1 out of 2

c.) 2 out of 3

d.) 3 out of 16

### Answers

**1. d) 4 out of 13.** This is a simple probability problem, since there is only one event happening: pulling out one piece of candy. The number of favorable outcomes is 4, since Billy wants to pull out a green apple candy, and there are 4 of these in the bag. That means there are four ways Billy could pull out a green apple candy. The number of possible outcomes is 13, since, if you add up all the candy in the bag, there are 13 pieces. So, the probability of Billy randomly pulling out a green apple candy is 4 out of 13.

**2. a) 1 out of 16.** This is a compound probability problem, since there are multiple events that need to happen in order for the outcome to be favorable. For compound probability, you multiply together the probability of each independent event. Since a quarter only has two sides, the likelihood of throwing a heads or a tails with any given toss is ^{1}⁄_{2}. There are four events: 1) throwing a heads 2) throwing a heads 3) throwing a tails 4) throwing a heads. The probability of each event individually is ^{1}⁄_{2}, so, to find the probability of all four of them happening, you need to calculate:

^{1}⁄_{2} × ^{1}⁄_{2} × ^{1}⁄_{2} × ^{1}⁄_{2}= ^{1}⁄_{16}

## Next Steps

Feeling confident? Put your newly honed math skills to the test by trying out a practice test.

Want to know more about probability? Khan Academy has a lesson on probability basics that includes helpful videos and examples.

For more GED prep, you should also check out our 5 Ways to Study for the GED Online.