What you should learn

To find the probability of a compound event

NCTM Curriculm Standards 5 - 10

 

In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:

Tree Diagram

Outcomes

Compound Event

Simple Events

Independent Events

Dependent Events

 

 

Introduction: A group of college students are planning a trip to visit Virgin Island National Park, where they will study the Carib Indian relics and the remnants of the forts build by the Danes. The Carib Indians were the original occupants of the islands, but had died or left by the early 1600s. The Danes formally claimed the islands in 1666, and they remained under Danish control until 1917.

The group's advisor must plan how the group will get to the Virgin Islands. From their college, they will travel to Miami, Florida, by car, bus, train, or plane. Then to travel to St. Thomas in the Virgin Islands, they could take a plane or a ship. Suppose the advisor picks a mode of transportation at random. What is the probability that they will travel by car first and then fly?

To calculate this probability, you need to know all of the possible ways to get to St. Thomas. One method for finding this out is to draw a tree diagram. The tree diagram below shows how to get from college to Miami and then to St. Thomas. The last column details all the possible combinations or outcomes of transportation.

Since the mode of transportation is chosen at random, you can assume that all combinations of travel are equally likely. Since there are 8 outcomes, the probability of traveling by car is first adn then flying is 1/8 or 0.125.

This problem is an example of finding the probability of a compound event. A compound event consists of two or more simple events. Choosing a car, plane, train, or bus for the first part of the trip is a simple event. Then, selecting a plane or ship for the second stage of the trip is another simple event. The selection of a mode of transportation for each part of the trip is a compound event.

Exercise 1: Use the tree diagram for the application at the beginning of the lesson to answer each question.

a. What is the probability that the group will take a ship to get to St. Thomas?

b. What is the probability that the group will travel by plane for both parts of the trip?

 

 

Refer to the application at the beginning of the lesson. Because one choice does not affect the others, we say these are independent events. If the outcome of an event does affect the outcome of another event, we say that these are dependent events.

Exercise 2: Booker T. Washington High School is having its annual Spring Carnival. The ninth grade class has decided to have a game booth. To win a small stuffed animal, a player will have to draw 2 marbles of the same color form a box containing 3 marbles - 1 red, 1 white, 1 yellow. First a marble is drawn, put back in the box, and then a second marble is drawn.

a. What are the possible outcomes?

b. What is the probability of winning the game?

 

 

Probability can also play an important role in determining the possible outcomes of a sporting event.

Exercise 3: The Rockets and the Knicks are going to play a best two out of three exhibition game series.

a. What are the possible outcomes?

b. Assuming that the teams are equally matched, what is the probability that the series will end in two games?

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: 9 - 17 odd, 19 - 23

Alternative Homework: Enriched: 8 - 16 even, 17 - 23

Extra Practice: Students book page 773 Lesson 7-5

Extra Practice Worksheet: Click Here.

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