Simple Events. chocolate? Write in simplest form. 1

Transcription

1 9 - Simple Events Cheesecake MAIN IDEA Find the probability of a simple event. New Vocabulary outcome simple event probability random complementary event Math Online original FOOD A cheesecake has four slices of each type as shown.. What fraction of the cheesecake is raspberry chocolate turtle chocolate? Write in simplest form.. Suppose your friend gives you the first piece of cheesecake without asking which type you prefer. Are your chances of getting original the same as getting raspberry? See Ch. 9 Answer Appendix. glencoe.com Concepts In Motion Extra Examples Personal Tutor Self-Check Quiz An outcome is any one of the possible results of an action. A simple event is one outcome or a collection of outcomes. For example, getting a piece of chocolate cheesecake is a simple event. The chance of that event happening is called its probability. Probability Words Symbols Key Concept If all outcomes are equally likely, the probability of a simple event is a ratio that compares the number of favorable outcomes to the number of possible outcomes. P(event) = number of favorable outcomes number of possible outcomes Find Probability What is the probability of rolling an even number on a number cube marked with,,,,, and on its faces? even numbers possible total numbers possible = or P(even number) = The probability of rolling an even number is,., or %. Use the number cube above to find each probability. Write as a a. P(odd number) Chapter 9 Probability b. P( or ) c. P(prime number)

2 Outcomes occur at random if each outcome occurs by chance. For example, rolling a number on a number cube occurs at random. TALENT COMPETITION Simone and her three friends were deciding how to pick the song they will sing for their school s talent show. They decide to roll a number cube. The person with the lowest number chooses the song. If her friends rolled a,, and, what is the probability that Simone will get to choose the song? The possible outcomes of rolling a number cube are,,,,, and. In order for Simone to be able to choose the song, she will need to roll a. Let P(A) be the probability that Simone chooses the song. number of favorable outcomes P(A) = number of possible outcomes = There are possible outcomes, and of them is favorable. The probability that Simone will choose the song is, or about 7%. MUSIC The table shows the New York Philharmonic numbers of brass instrument Brass Instrument Players players in the New York Horn Philharmonic. Suppose one Trombone brass instrument player is Trumpet randomly selected to be a featured performer. Find the Tuba probability of each event. Write Source: New York Philharmonic as a d. P(trumpet) e. P(brass) f. P(flute) g. P(horn or tuba) The probability that an event will happen can be any number from to, including and, as shown on the number line below. Notice that probabilities can be written as fractions, decimals, or percents. Impossible Unlikely As likely to happen as not Likely Certain...7 % % % 7% % Lesson 9- Simple Events

3 Either Simone will go first or she will not go first. These two events are complementary events. The sum of the probabilities of an event and its complement is or %. In symbols, P(A) + P(not A) =. Complement of an Event The probability that event A will not occur is noted as P(not A ). Since P(A ) + P(not A ) =, P(not A ) = - P(A ). P(not A ) is read as the probability of the complement of A. Complementary Events TALENT COMPETITION Refer to Example. Find the probability that Simone will not choose the song. The probability that Simone will not choose the song is the complement of the probability that Simone will choose the song. P(A) + P(not A) = - Definition of complementary events + P(not A) = Replace P(A) with. - Subtract from each side. is P(not A) = - - or The probability that Simone will not choose the song is, or about %. SCHOOL Ramón s teacher uses a spinner similar to the one shown at the right to determine the order in which each group will make their presentation. Use the spinner to find each probability. Write as a h. P(not group ) i. P(not group or group ) indicates multi-step problem Example (p. ) Examples, (pp. ) Use the spinner to find each probability. Write as a. P(M). P(Q or R). P(vowel) MARBLES Robert has a bag that contains 7 blue, purple, red, and orange marbles. Find each probability if he draws one marble at random from the bag. Write as a. P(purple) 7. P(not blue). P(red or orange). P(not red or orange) S R. P(green) T Q M 9. P(not yellow) P N O Example (p. ) Chapter 9 Probability. SURVEYS Shanté asked her classmates how many pets they own. The responses are in the table. If a student in her class is selected at random, what is the probability that the student does not own or more pets? Number of Pets Response None or more

4 HOMEWORK HELP For Exercises 7, HELP See Examples Exercise Levels: A: B: 7 C: A set of cards is numbered,,,...,. Suppose you pick a card at random without looking. Find the probability of each event. Write as a. P(). P( or ). P(even number). P(not ) 9 RAFFLE The table shows those students in seventh grade who entered in the school drawing to win lunch with the principal. Suppose that only one student is randomly selected to win. Find the probability of each event. Write as a 7. P(girl) 9. P(Room ) 7. P(boy). P(Room ). P(girl or boy). P(Room ). P(multiple of ). P(not a factor of ) Lunch Raffle girls boys Room Room Room. P(not Room ). P(Room or ). SOUP A cupboard contains soup cans. Seven are tomato, are cream of mushroom, are chicken, and are vegetable. If one can is chosen at random from the cupboard, what is the probability that it is neither cream of mushroom nor vegetable soup? Write as a percent. %. VIDEOS In a drawing, one name is randomly chosen from a jar of 7 names to receive free video rentals for a month. If Enola entered her name times, what is the probability that she is not chosen to receive the free rentals? Write as a 7 7. PETS The graph shows the last types of pets that were purchased at a local pet store. Based on this, what is the probability that the next pet purchased will be a dog? Write as a. GAMES For a certain game, the probability of choosing a card with the number is.. What is the probability of not choosing card? WEATHER The forecast for tomorrow says that there is a 7% chance of rain. Describe the complementary event and predict its probability. See margin. 7 Number Purchased Dogs Cats Pet Store 9 Birds Snakes Gerbils Type of Pet PRACTICE EXTRA PRACTICE See pages 9, 7.. ANNOUNCEMENTS There are 9 students in the seventh grade. Fifty-two of those students are girls. If one student will be chosen at random to read the morning announcements for the week, what is the probability that the 9 student is a boy? Lesson 9- Simple Events

5 H.O.T. Problems. See margin.. REASONING A leap year has days and occurs in non-century years that are evenly divisible by. The extra day is added as February 9th. Determine whether each probability is or. Explain your reasoning. a. P(there will be 9 days in February in ) b. P(there will be 9 days in February in ). CHALLENGE A bag contains red marbles, blue marbles, and green marbles. How many marbles of each color should be added so that the total number of marbles is 7, but the probability of randomly selecting one marble of each color remains unchanged? Explain your reasoning.. Which One Doesn t Belong? Identify the pair of probabilities that does not represent probabilities of complementary events. Explain your reasoning.,.,,.,.. See Ch. 9 Answer Appendix. WRITING IN. MATH Marissa has black T-shirts, purple T-shirts, and orange T-shirt. Without calculating, determine whether each of the following probabilities is reasonable if she randomly selects one T-shirt. Explain your reasoning. a. P(black T-shirt) = b. P(orange T-shirt) = c. P(purple T-shirt) =. A bag contains blue marbles, red marbles, yellow marbles, and brown marbles. If a marble is randomly selected, what is the probability that it will be brown? C A.7 C. B % D. What is the probability of the spinner landing on a number less than? G F % H % G 7.% J 7% 7 7. RAIN The scatter plot shows the relationship between rainfall and lawn growth. Why might the graph be misleading? (Lesson -9) There are no labels on the vertical scale.. PARKS A researcher randomly selected households near a city park. Of these, % said they visit the park daily. If there are households near the park, about how many visit it daily? (Lesson -) about households Height of Grass (in.) Rainfall and Lawn Growth y PREREQUISITE SKILL Write each (Lesson -) x Amount of Rain (in.) 9 Chapter 9 Probability