Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Solve each proportion. 1. = 2. = 3. = 4. = x 5.1 6 1.7 24 108 n 9 18 2 65 0.1 13 x 46 n 200 46 0.02 10.58

Problem of the Day Aiden is playing a board game using two six-sided number cubes. He wins if he doesn’t roll a six or a seven. What is the probability that Aiden will win on his next turn? 25 36

Learn to use probability to make decisions and predictions.

Additional Example 1A: Using Probability to Make Decisions and Predictions The table shows the satisfaction rating in a business’s survey of 500 customers. Of their 240,000 customers, how many should the business expect to be unsatisfied? Pleased Satisfied Unsatisfied 125 340 35 Find the probability of unsatisfied customers in the survey. number of customers unsatisfied in survey total number of customers surveyed 35 500 7 100 = or

Additional Example 1A Continued 7 100 t n t 240,000 = Set up a proportion. 7 x 240,000 = 100n Find the cross products. 1,680,000 = 100n t 100 100 Divide both sides by 100. 16,800 = n The business should expect to have 16,800 unsatisfied customers.

number of possible outcomes total possible outcomes Additional Example 1B: Using Probability to Make Decisions and Predictions Jared randomly draws a card from a 52-card deck and tries to guess what it is. If he tried this trick 1040 times over the course of his life, what is the best prediction for the amount of times it works? Find the theoretical probability of successful trick attempts. number of possible outcomes total possible outcomes 1 52 =

Additional Example 1B Continued 1 52 t n t 1040 = Set up a proportion. 1  1040 = 52n Find the cross products. 1040 = 52n t 52 52 Divide both sides by 52. 20 = n The trick would work about 20 times.

Check It Out: Example 1A The table shows the satisfaction rating in a business’s survey of 500 customers. Of their 240,000 customers, how many should the business expect to be pleased? Pleased Satisfied Unsatisfied 125 340 35 Find the probability of pleased customers in the survey. number of customers pleased in survey total number of customers surveyed 125 500 1 4 = or

Check It Out: Example 1A Continued 1 4 t n t 240,000 = Set up a proportion. 1  240,000 = 4n Find the cross products. 240,000 = 4n t 4 4 Divide both sides by 4. 60,000 = n The business should expect to have 60,000 pleased customers.

number of possible outcomes total possible outcomes Check It Out: Example 1B Kaitlyn randomly draws a domino tile from an 18 piece set and tries to guess what it is. If she tries this trick 2250 times over the course of her life, what is the best prediction for the amount of times it works? Find the theoretical probability of successful trick attempts. number of possible outcomes total possible outcomes 1 18 =

Check It Out: Example 1B Continued 1 18 t n t 2250 = Set up a proportion. 1 x 2250 = 18n Find the cross products. 2250 = 18n t 18 18 Divide both sides by 18. 125 = n The trick would work approximately 125 times.

Additional Example 2: Deciding Whether a Game is Fair In a game, two players each flip a coin. Player A wins if exactly one of the two coins is heads. Otherwise, player B wins. Determine whether the game is fair. List all possible outcomes. HH HT TT TH Find the theoretical probability of each player’s winning. 1 2 There are 2 possibilities with exactly 1 coin as heads. P(player A winning) = 1 2 P(player B winning) = Since = , the game is fair. 1 2

List all possible outcomes. HH HT TT TH Check It Out: Example 2 In a new game, two players each flip a coin. Player A wins if at least one of the two coins is heads. Otherwise, player B wins. Determine whether the game is fair. List all possible outcomes. HH HT TT TH Find the theoretical probability of each player’s winning. 3 4 There are 3 possibilities with at least 1 coin as heads. P(player A winning) = 1 4 P(player B winning) = Since ≠ , the game is not fair. 1 4 3 4

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 15

Lesson Quiz: Part I 1. Out of the 35 products a salesperson sold last week, 8 of them were products worth over $200. About how many of these products should the salesperson expect to sell if he has 140 customers next month? 2. A student answers all 12 multiple choice questions on a quiz at random. Each multiple choice question has 4 choices. What is the best guess for the amount of multiple choice questions the student will answer correctly? 32 3

Lesson Quiz: Part II 3. In a game, two players each roll a 6-sided number cube and add the two numbers. If the roll is a 6 or less, player A wins. If the roll is 8 or more, player B wins. if the roll is a 7, the players tie and roll again. Is this a fair game? Yes

Lesson Quiz for Student Response Systems 1. Last week 40 babies were born in a hospital, of whom 25 were male. If the hospital expects 264 babies to be born next month, how many would be male? A. 25 B. 155 C. 165 D. 422 18

Lesson Quiz for Student Response Systems 2. A card is chosen at random from a well shuffled 52-card deck, the suit is recorded and replaced. This experiment is repeated 520 times. What is the best prediction for the number of times that a spade will be chosen? A. 260 B. 173 C. 130 D. 104 19

Lesson Quiz for Student Response Systems 3. Identify a fair game. A. Two players flip a coin each. Player A wins if both the coins land with heads. Otherwise player B wins. B. Player A flips a coin and player B rolls a 6-sided number cube. Player A wins if the cube shows an even number. Otherwise player B wins. C. Player A rolls a 6-sided number cube and player B flips a coin. Player A wins if the coin lands on heads and the cube shows an even number. Otherwise player B wins. D. Two players each roll a 6-sided number cube and add the numbers. Player A wins if the total is less than four. Otherwise player B wins. 20