## Lesson: Probability

Introducing the Concept

**Materials:** 12 cardboard cards with the following letters: 4 with an A, 2 with an E, 2 with an I, 3 with an O, and 1 with a U

**Prerequisite Skills and Concepts:** Students should be able to simplify fractions.

**Say:***You have learned how to list all possible outcomes. Now you will learn how to express probability as a fraction.***Say:***We have 12 cards, all the same size and shape, with the following letters printed on them: 4 with an A, 2 with an E, 2 with an I, 3 with an O, and 1 with a U. We will shuffle the cards and choose one at random.*

Write the following on the board to clarify the numbers for the students:A = 4 E = 2 I = 2 O = 3 U = 1. **Say:***We will try to find the probability of choosing an E.***Ask:***How many cards are there altogether?*(12)**Ask:***To write the probability as a fraction, what denominator do we use and why?*

Students should say “12,” because it represents the total number of outcomes or cards we could choose.**Ask:***Out of 12 possible outcomes, how many favorable outcomes are there for “E?”*

Students should respond that there are 2 cards marked E and thus there are 2 favorable outcomes.**Say:***So the numerator of the fraction is 2.***Say:***The definition of probability is “the likelihood of an event occurring.” This is shown as the ratio of the number of favorable outcomes to the number of possible outcomes.*

Write the following on the board.**Ask:***What fraction should we write for the probability of drawing an E?*Students should respond with , or . Remind students that when we express probability as a fraction, we write the fraction in simplest form.**Ask:***If we shuffle all 12 cards again, what is the probability that we will draw a card with an O?*

Students should respond , or .**Ask:***What is the probability of drawing a card with a consonant on it?*

Students should respond that the probability is zero ( = 0), since the cards list only vowels. Therefore, it is impossible to draw a card with a consonant on it.**Ask:***What is the probability of drawing a card with a vowel on it?*

Students should reply that the probability is 1, since all cards have vowels. ( = 1) This is a certain event.**Ask:***Is the probability of drawing an A or an E likely, unlikely, or equally likely?*

Students should respond that the drawing of an A or an E is equally likely. The number of favorable outcomes is 4 + 2, or 6, with a probability of 6 out of 12, or , which is .Have students use a number cube marked 1, 3, 5, 7, 9, and 11. Have them find the probability of rolling the cube and having the following land faceup. Solutions are provided.

- 3—
- number less than 10—
- number between 2 and 6—
- number less than 34—1
- number greater than 4 and less than 11—