# Exclusive, Independent, and Complement Events Worksheets

What Are Exclusive, Independent, and Complement Events in Probability? Probability is a branch of mathematics that defines the likelihood of an occurrence of an event and describes if the proposition is true or not. It is a number between 0 and 1 where one defines the certainty of occurrence, and zero represents the impossibility of occurrence of an event. If the number is nearer to 1 like 0.8, then the event is more likely to happen. However, if the number is closer to 0 like 0.2 then the event is less likely to occur. In probability, the events can be classified as independent, exclusive, and complementary. Independent Event - In probability, two events are independent if they do not affect or influence the occurrence of each other. However, if the occurrence of one event affects the incidence of others, then they are dependent events. Exclusive Events - In probability, two events are exclusive when they cannot take place at the same time. It means that the incidence of one event prevents the other event from taking place. For example, if you get 'tail' on a coin toss, you cannot 'head' at the same time. Hence, this event is an exclusive event. Complementary Event - Complementary events are those that have two outcomes, each being the complement or opposite of one another. For example, it rains, or it does not rain.

• ### Basic Lesson

Introduces the concept of mutually exclusive and complementary events. One card is drawn from a standard deck of cards. Find the odds of drawing a red card or a ten.

• ### Intermediate Lesson

This lesson focuses on independent events. You randomly choose a red ball and then a blue ball from the same jar without replacement. Are these two events dependent or independent? Here choosing of blue ball is affected by choosing of red ball without replacement, as number of total balls get reduced. Two events are said to be independent if the result of the second event is not affected by the result of the first event.

• ### Independent Practice 1

Students practice with 20 Exclusive, Independent, and Complement Events problems. The answers can be found below. Getting an even number on the number cube and spinning red color on the spinner. Is this independent event?

• ### Independent Practice 2

Another 20 Exclusive, Independent, and Complement Events problems. The answers can be found below. There are 26 tiles of which 5 represent vowels in a game of scrabble. Two tiles are drawn so that the first is replaced before the second is drawn. What is the probability of not getting a consonant both the times?

• ### Homework Worksheet

Reviews all skills in the unit. A great take home sheet. Also provides a practice problem. A number is selected from 1 to 20 at random. What is the complement of getting a number multiple of 5?

• ### Skill Quiz

10 problems that test Exclusive, Independent, and Complement Events skills. Drawing a ten and drawing a jack from a standard deck of cards. Are these events mutually exclusive?

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.