Overview

Students create a table to determine the probability of two events happening together (compound probability). They learn the definitions of complementary events, independent events, dependent events and compound events.

Objective

Students will be able to demonstrate an understanding of compound events.

Standards Addressed

Mathematics — Data Analysis

Grade 7

Probability, Benchmark I

07. Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams and area models.

 

Grade 8

Probability, Benchmark J

11. Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities.

 

Materials

• Large model of a die

• Coin

Procedure

1. Review the following definition of probability:

P(event) =	possibility of event
	total possible outcomes

2. Review tree diagrams, experimental vs. theoretical probability, the concept of certainty vs. impossibility and the fact that probability is shown as a fraction or decimal between 0 and 1.

3. Have a large die that the students can see as they answer the following questions.

   Write the sample space for tossing this die. Answer: 1, 2, 3, 4, 5 and 6.

   The probability of rolling each number on the die is P(1) = 1⁄6; P(2) = 1⁄6, etc. Ask the students if the probability of rolling a one is one in six, then what would be the probability of not getting a one? Answer: P(not 1) = 5⁄6. This is called the complement of the event. When two complementary events are added together, they must equal one.

   Ask what the probability would be of rolling a seven on this die. Answer: P(7) = 0⁄6 or 0. This would be called an impossibility.

4. Ask the students to tell what the words dependent and independent mean. Answer: Dependent means conditioned or determined by something else or contingent upon. Independent means not influenced or controlled by others or standing alone.

5. Give the student theses two scenarios:

   I’m going to the movies if it rains on Tuesday.
   
   I’m going to the movies on Tuesday whether it rains or not.
   
   Ask which is dependent and which is independent. Answer: A is dependent because attending the movie depends on whether or not it rains. B is independent because both going to the movies and whether it rains or not are stand-alone events.

6. Review compound events — when two or more independent events are thought of as a single unit. Have the students figure out the probability of throwing a one on the die along with tossing heads with a coin. Give them about five minutes to figure it out and then ask someone to explain how they got the answer. Answer: Students can use a variety of ways to solve this problem. A tree diagram is one way. P = 1⁄6 x 1⁄2 = 1⁄12. So theoretically, you should roll a one on a die plus get heads when a coin is tossed once in every 12 times. This is a compound event.

7. Have the students compute one more example. A girl has three sweaters: red, blue and yellow. She has two pairs of pants: jeans and shorts. What is the probability that she will choose a red sweater and jeans? Answer: P(red sweater and jeans) = 1⁄3 x 1⁄2 = 1⁄6.

8. Remind the students that to find the compound probability, you would multiply the probability of the two independent events.

9. Review the concept of using a geometric shape to help you solve the problem (area models).

10. Have the students work with a partner on the Compound Probability student sheet. If you think they will have difficulty with this concept, you could do Box A with them.

Evaluation

There are 16 possible answers that the student could get right or wrong on this sheet. A percentage of the number correct would be one way of giving a grade for this worksheet. View the Compound Probability Answers (PDF file).