Counting Outcomes and Theoretical Probability

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

3. mayonnaise Each branch of the “tree” represents one choice—for example, wheat-ham-mayonnaise. ham mustard wheat mayonnaise turkey mustard mayonnaise ham mustard white mayonnaise turkey mustard Counting Outcomes and Theoretical Probability PRE-ALGEBRA LESSON 12-4 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. There are 8 possible sandwich choices. Quick Check 12-4

4. 1st digit outcomes 10 2nd digit outcomes 10 3rd digit outcomes 10 4th digit outcomes 10 5th digit outcomes 10 total outcomes = 100,000 • • • • number of favorable outcomes number of possible outcomes P(winning number) = = 1 20,000 The probability is , or . 5 100,000 5 100,000 Counting Outcomes and Theoretical Probability PRE-ALGEBRA LESSON 12-4 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? First find the number of possible outcomes. For each digit, there are 10 possible outcomes, 0 through 9. Then find the probability when there are five favorable outcomes. Quick Check 12-4

5. 1 6 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? 12 125 12-4

6. 4 7 5 9 3 6 2 4 4 8 1 5 3 5 8 9 1 4 9 10 2 10 4 10 Independent and Dependent Events PRE-ALGEBRA LESSON 12-5 (For help, go to Lesson 5-4.) Multiply. 1. • 2. • 3. • 4. • 5. • 6. • Check Skills You’ll Need 12-5

7. 1 8 2 7 4 5 5 18 8 100 72 90 2 16 12 42 20 72 3 25 2 25 Independent and Dependent Events PRE-ALGEBRA LESSON 12-5 Solutions 1. 2. 3. 4. 5. 6. = = = = = 12-5

8. 1 6 P(5) = There is one 5 among 6 numbers on a number cube. 3 6 P(less than 4) = There are three numbers less than 4 on a number cube. P(5, then less than 4) = P(5) • P(less than 4) 1 6 3 6 = • 3 36 1 12 1 12 = , or The probability of rolling 5 and then a number less than 4 is . Independent and Dependent Events PRE-ALGEBRA LESSON 12-5 Quick Check 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? 12-5

9. 2 5 P(boy) = Two of five students are boys. If a boy’s name is drawn, one of the four remaining students is a boy. 1 4 P(boy after boy) = 2 5 1 4 Substitute. = • 2 20 1 10 1 10 Simplify. = , or The probability that both representatives will be boys is . Independent and Dependent Events PRE-ALGEBRA LESSON 12-5 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? P(boy, then boy) = P(boy) • P(boy after boy) Quick Check 12-5

10. 1 12 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% 12-5

11. 7 22 5 33 ; Independent and Dependent Events PRE-ALGEBRA LESSON 12-5 Solve. 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? 12-5