1. Counting Outcomes and Theoretical Probability PRE-ALGEBRA LESSON 12-4 (For help, go to Lesson 6-4.) A bag has 5 blue (B) chips, 4 red (R) chips, and 3 tan (T) chips. Find each probability for choosing a chip at random from the bag. 1.P(R)2.P(not R)3.P(B) 4.P(R or B)5.P(T)6.P(B or T) Check Skills You’ll Need 12-4

2. Counting Outcomes and Theoretical Probability PRE-ALGEBRA LESSON 12-4 Solutions 1. 2. 3. 4. 5. 6. favorable outcomes all possible outcomes = drawing a blue chip 12 = 5 12 1313 4 12 favorable outcomes all possible outcomes = drawing a red chip 12 == favorable outcomes all possible outcomes = drawing a chip that is not red 12 = 8 12 = 2323 favorable outcomes all possible outcomes = drawing a red or blue chip 12 = 9 12 = 3434 favorable outcomes all possible outcomes = drawing a tan chip 12 = 3 12 = 1414 favorable outcomes all possible outcomes = drawing a blue or tan chip 12 = 8 12 = 2323 12-4

3. Counting Outcomes and Theoretical Probability The school cafeteria sells sandwiches for which you can choose one item from each of the following categories: two breads (wheat or white), two meats (ham or turkey), and two condiments (mayonnaise or mustard). Draw a tree diagram to find the number of sandwich choices. PRE-ALGEBRA LESSON 12-4 There are 8 possible sandwich choices. mayonnaise Each branch of the “tree” represents one choice—for example, wheat-ham- mayonnaise. wheat white ham turkey ham turkey mayonnaise mustard mayonnaise mustard mayonnaise mustard Quick Check 12-4

4. Counting Outcomes and Theoretical Probability In some state lotteries, the winning number is made up of five digits chosen at random. Suppose a player buys 5 tickets with different numbers. What is the probability that the player has a winning number? PRE-ALGEBRA LESSON 12-4 First find the number of possible outcomes. For each digit, there are 10 possible outcomes, 0 through 9. 1st digit outcomes 10 2nd digit outcomes 10 3rd digit outcomes 10 5th digit outcomes 10 4th digit outcomes 10 total outcomes = 100,000 Then find the probability when there are five favorable outcomes. P(winning number) = = number of favorable outcomes number of possible outcomes 5 100,000 5 100,000 The probability is, or. 1 20,000 Quick Check 12-4

5. Counting Outcomes and Theoretical Probability PRE-ALGEBRA LESSON 12-4 Use the following information for Questions 1 and 2. In a game, a number cube is tossed to determine the number of spaces to move, and a coin is tossed to determine forward or backward movement. 1.How many possible outcomes are there? 2.What is the theoretical probability you will move four spaces? 3.How many different three-digit whole numbers are possible using the digits 1, 2, 3, 4, and 5? 125 12 1616 12-4

6. Independent and Dependent Events PRE-ALGEBRA LESSON 12-5 (For help, go to Lesson 5-4.) Multiply. 1.2.3. 4.5.6. 3535 1515 1414 2424 4747 3636 5959 4848 4 10 2 10 9 10 8989 Check Skills You’ll Need 12-5

7. Independent and Dependent Events PRE-ALGEBRA LESSON 12-5 Solutions 1.2.3. 4.5.6. 5 18 3 25 20 72 = 1818 2 16 = 2727 12 42 = 4545 72 90 = 8 100 2 25 = 12-5

8. Independent and Dependent Events PRE-ALGEBRA LESSON 12-5 You roll a number cube once. Then you roll it again. What is the probability that you get 5 on the first roll and a number less than 4 on the second roll? The probability of rolling 5 and then a number less than 4 is. 1 12 P(5, then less than 4) = P(5) P(less than 4) = 1616 3636 3 36 1 12 =, or P(5) = 1616 There is one 5 among 6 numbers on a number cube. P(less than 4) = 3636 There are three numbers less than 4 on a number cube. Quick Check 12-5

9. Independent and Dependent Events Three girls and two boys volunteer to represent their class at a school assembly. The teacher selects one name and then another from a bag containing the five students’ names. What is the probability that both representatives will be boys? PRE-ALGEBRA LESSON 12-5 P(boy, then boy) = P(boy) P(boy after boy) The probability that both representatives will be boys is. 1 10 2 20 1 10 =, or Simplify. = 2525 1414 Substitute. P(boy after boy) = 1414 If a boy’s name is drawn, one of the four remaining students is a boy. P(boy) = 2525 Two of five students are boys. Quick Check 12-5

10. Independent and Dependent Events PRE-ALGEBRA LESSON 12-5 Solve. 1.You roll a number cube once. Then you roll it again. What is the probability that you get 6 on the first roll and a number greater than 3 on the second roll? 2.Suppose there are three white marbles and three black marbles in a bag and you want to remove two marbles. What is the probability that you will select a white marble and then a black marble? Express your answer as a percent. 30% 1 12 12-5

11. Independent and Dependent Events PRE-ALGEBRA LESSON 12-5 Solve. 7 22 5 33 ; 12-5 3.Each of five girls and seven boys wants to be one of the two announcers for a variety show. To be fair, a teacher puts the names of the twelve students in a hat and draws two. What is the probability that the teacher will draw the names of two boys? Of two girls?