When a number cube is rolled once, the possible numbers that could show face up are

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1 C3 Chapter 12 Understanding Probability Essential question: How can you describe the likelihood of an event? Example 1 Likelihood of an Event When a number cube is rolled once, the possible numbers that could show face up are. Each time you roll the cube, a number lands face up. This is called an event. Below is a list of 9 different events. Work with a partner to order the events from those least likely to happen to the ones that are most likely to happen when you roll the number cube one time. Use the space next to each event to write any notes that might help you order them. Some may be equally as likely as others; give them the same number if that occurs. Rolling a number less than 7 Rolling an 8 Rolling a 1, 2, or 3 Rolling a 5 Rolling a number other than 6 Rolling an even number Rolling a number greater than 5 Rolling an odd number Rolling a prime number Now answer the following questions: 1) How did you sort the events? 2) Are any of the events impossible? Why were they impossible?

2 An experiment is an activity involving chance in which results are observed. Each observation of an experiment is a trial, and each result is an outcome. A set of one or more outcomes is an event. The probability of an event, written P(event), measures the likelihood that the event will occur. Probability is a measure between 0 and 1 as shown on the number line and can be written as a fraction, a decimal, or percent. If the event is not likely to occur very many times, the probability of the event is close to 0. Likewise, if an event is likely to occur many times, the event s probability is closer to 1. Example 2 Describing Events Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. Include the associated fraction, decimal or percent. A) You flip a coin. The coin lands tails up. B) You roll two number cubes and the sum of the numbers is 11. C) A bowl contains 14 red marbles and 3 green marbles. You pick a red marble. D) A spinner has 10 equal sections marked 1 through 10. You spin and land on a number greater than 0. Now You Try It! Describe each event as impossible, unlikely, as likely as not, likely, or certain. Include the associated fraction, decimal or percent. 1) A hat contains pieces of paper marked with the numbers 1 through 20. You pick an even number. 2) A spinner has 8 equal sections marked 1 through 8. You spin and land on 0.

3 3) The probability of event A is. The probability of event B is. What can you conclude about the two events? The complement of an event is the set of all outcomes not included in the event. For example, consider the event that you roll a number cube and get a 3. The complement is the event that you do not roll a 3. The complement is rolling a 1, 2, 4, 5, or 6. The sum of the probabilities of an event and its complement equals 1. P(event) + P(complement) = 1 Example 3 Using the Complement of an Event Describe a standard deck of cards: In a standard deck of cards, the probability of choosing a card at random and getting an Queen is. What is the probability of not getting an Queen? P(event) + P(complement) = P(Queen) + P ( ) = 1 + P( ) = 1 P(not getting a Queen) = 1 = Now You Try It! 1) A jar contains marbles marked with the numbers 1 through 10. The probability that you pick a number at random and get a 5 is. A) What is the complement of this event? B) What is the probability of the complement?

4 2) You roll a six-sided number cube. The probability that you roll an odd number is. A) What is the complement of this event? B) What is the probability of the complement? 3) Why do the probability of an event and the probability of its complement add up to 1? 4) Give an example of a real-world event and its complement. PRACTICE: 1) Define each of the following in your own words: Experiment Trial Outcome Event Probability Probability is a measure between and. Complement of an event P(event) + P(complement) =

5 2) In a hat, you have cards with the numbers 1 through 20 written on them. You pick one card at random. Order the events from least likely to happen to most likely to happen. greater than 0. You pick an even number. that is at least 8. that is at most 0. Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. Include the associated fraction, decimal or percent. 3) randomly picking a purple card from a standard deck of playing cards 4) randomly picking a black card from a standard deck of playing cards 5) picking a number less that 20 from a jar with papers labeled from 1 to 10 6) picking a number that is divisible by 5 from a jar with papers labeled from 1 to 15 7) The probability of rolling a 5 on a number cube is. What is the probability of not rolling a 5? 8) The probability that a coin will land heads up when flipping a coin is. What is the probability of getting tails? 9) The probability of spinning a 4 on a spinner with 8 equal sections marked 1 through 8 is. What is the complement of this event? What is the probability of the complement? 10) The probability of picking a King from a standard deck of cards is. What is the complement of this event? What is the probability of the complement? 11) Describe an event that has a probability of 0% and an event that has a probability of 100%.