Compound Events

A simple event consists of just one outcome, while a compound event consists of two or more simple events. For example, tossing a coin is a simple event, but if we roll a die at the same time, this combination of two simple events counts as a compound event instead.

How do we find the probability of a compound event?

If we wanted to find the probability of getting an even number when rolling a six-sided die, the probability is simply one-half or

, since half of the numbers are even.

If we want to calculate the probability of a compound event, we have three options:

• Organized lists
• Tree diagrams
• Tables

Organized lists

When you write an organized list, you simply write out all of the possible outcomes of a compound event. If we rolled a die and flipped a coin, we could write the following list:

1−H, 2−H, 3−H, 4−H, 5−H, 6−H, 1−T, 2−T, 3−T, 4−T, 5−T, and 6−T, where H = heads and T = tails.

If we wanted to find out the probability of rolling heads and either 1, 2, or 3, we would simply find the fraction of the favorable outcome. This is:

or

Tree diagrams

We can also create tree diagrams to help us visualize the possibilities.

We start by mapping out the first event:


Then, we add the possibilities of the second event:


If we wanted to flip two coins simultaneously, we might get a tree diagram like this:

Tables

We can also write out the sample space using tables. This essentially involves turning our organized list into a table with a numbered list of the total events or "rolls" on the left-hand side.

Outcome	Probability
1-H	1/12
2-H	1/12
3-H	1/12
4-H	1/12
5-H	1/12
6-H	1/12
1-T	1/12
2-T	1/12
3-T	1/12
4-T	1/12
5-T	1/12
6-T	1/12

Then, if you were interested in what is the probability of rolling an odd number and a tails, you go to the table and find all the options that fit the condition, 1-T, 3-T, 5-T and then sum the given probabilities,

Topics related to the Compound Events

Complement of an Event

Multiplication Rule of Probability

Probability

Flashcards covering the Compound Events

Statistics Flashcards

Common Core: High School - Statistics and Probability Flashcards

Practice tests covering the Compound Events

Probability Theory Practice Tests

Common Core: High School - Statistics and Probability Diagnostic Tests

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