12 1 Introduction to Probability Warm Up Write

12 -1 Introduction to Probability Warm Up Write each fraction as a decimal and as a percent. 3 __ 1. 4 0. 75; 75% 1 __ 2. 2 0. 50; 50% __ 2 __ 3. 9 0. 2; 22. 2% 3 __ 4. 8 0. 375; 37. 5% Course 1

12 -1 Introduction to Probability Learn to estimate the likelihood of an event and to write and compare probabilities. Course 1

12 -1 Introduction Insert Lesson Here to. Title Probability Vocabulary probability Course 1

12 -1 Introduction to Probability is the measure of how likely an event is to occur. Course 1

12 -1 Introduction to Probability Probabilities are written as fractions or decimals from 0 to 1 or as percents from 0% to 100%. The higher an event’s probability, the more likely that event is to happen. • Events with a probability of 0, or 0%, never happen. • Events with a probability of 1, or 100%, always happen. • Events with a probability of 0. 5, or 50%, have the same chance of happening as of not happening. Course 1

12 -1 Introduction to Probability Impossible 0 0% Unlikely As likely as not 0. 5 1 __ 2 50% Course 1 Likely Certain 1 100%

12 -1 Introduction Insert Lesson Here to. Title Probability Example 1: Estimating the Likelihood of an Event Write impossible, unlikely, as likely as not, likely, or certain to describe each event. A. You roll an even number on a standard number cube. as likely as not B. February has 28 days. certain Helpful Hint A standard number cube is numbered from 1 to 6. Course 1

12 -1 Introduction Insert Lesson Here to. Title Probability Example 2: Estimating the Likelihood of an Event Write impossible, unlikely, as likely as not, likely, or certain to describe each event. C. This spinner lands on blue. unlikely D. This spinner lands on an odd number. impossible Course 1

12 -1 Introduction Insert Lesson Here to. Title Probability Example 3 Write impossible, unlikely, as likely as not, likely, or certain to describe each event. A. You guess a number between 1 and 1, 000. unlikely B. You will roll an odd number on a standard number cube. as likely as not Helpful Hint A standard number cube is numbered from 1 to 6. Course 1

12 -1 Introduction Insert Lesson Here to. Title Probability Example 4 Write impossible, unlikely, as likely as not, likely, or certain to describe each event. C. This spinner lands on green. unlikely D. This spinner lands on an even number. certain Course 1

12 -1 Introduction Insert Lesson Here to. Title Probability Example 5: Writing Probabilities A. The weather report gives a 75% chance of snow. Write this probability as a decimal and as a fraction. 75% = 0. 75 Write as a decimal. 75 3 Write as a fraction in 75% = ___ = __ simplest form. 100 4 B. The chance of being chosen is 0. 8. Write this probability as a fraction and as a percent. 8 4 __ __ 0. 8 = = 10 5 0. 8 = 80% Course 1 Write as a fraction in simplest form. Write as a percent.

12 -1 Introduction Insert Lesson Here to. Title Probability Example 6 A. The weather report gives a 25% chance of snow. Write this probability as a decimal and as a fraction. 25% = 0. 25 Write as a decimal. 25 1 Write as a fraction in 25% = ___ = __ simplest form. 100 4 B. The chance of being chosen is 0. 6. Write this probability as a fraction and as a percent. 6 3 __ __ 0. 6 = = 10 5 0. 6 = 60% Course 1 Write as a fraction in simplest form. Write as a percent.

12 -1 Introduction Insert Lesson Here to. Title Probability Example 7: Comparing Probabilities On a standard number cube, there is a 50% 1 % chance of rolling a multiple of 2 and a 33 __ 3 chance of rolling a multiple of 3. Is it more likely to roll a multiple of 2 or a multiple of 3? 1 Compare: 33 __% < 50% 3 It is more likely to roll a multiple of 2. Course 1

12 -1 Introduction Insert Lesson Here to. Title Probability Example 8: Comparing Probabilities When you spin a certain spinner, there is a 15% chance that it will land on yellow, a 15% chance it will land on green, and a 70% chance that it will land on purple. Is it more likely to land on purple or on green? Compare: 70% > 15% It is more likely to land on purple than on green. Course 1

12 -1 Introduction Insert Lesson to. Title Probability Here Lesson Quiz Write impossible, unlikely, as likely as not, likely, or certain to describe each event. 1. The sun will rise tomorrow. certain 2. You will roll 13 when rolling two dice. impossible 3. There is a 0. 125 chance of picking the winning ticket. Write this probability as a fraction and as 1 , 12. 5% a percent. __ 8 4. At Hamburger Hut, there is a 20% chance of getting a plastic dinosaur cup and a 35% chance of getting a plastic rabbit cup. It is less likely that you will receive a rabbit cup or dinosaur cup? dinosaur cup Course 1

12 -4 Theoretical Probability Learn to find theoretical probability and complement of an event. Course 1

12 -4 Theoretical Probability Another way to estimate probability of an event is to use theoretical probability. One situation in which you can use theoretical probability is when all outcomes have the same chance of occurring. In other words, the outcomes are equally likely. Course 1

12 -6 Theoretical Probability An experiment with equally likely outcomes is said to be fair. You can usually assume that experiments involving items such as coins and number cubes are fair. Course 1

12 -4 Theoretical Probability Example 1: Finding Theoretical Probability What is the probability of this fair spinner landing on 3? There are three possible outcomes when spinning this spinner: 1, 2, or 3. All are equally likely because the spinner is fair. P(3)= _________ 3 possible outcomes There is only one way for the spinner to land on 3. 1 way event can occur 1 __ _________ = P(3)= 3 possible outcomes 3 Course 1

12 -4 Theoretical Probability Example 2: Finding Theoretical Probability What is the probability of rolling a number greater than 4 on a fair number cube? There are six possible outcomes when a fair number cube is rolled: 1, 2, 3, 4, 5, or 6. All are equally likely. There are 2 ways to roll a number greater than 4: 5 or 6. P(greater than 4)= _________ 6 possible outcomes 2 ways events can occur __ 1 __________ P(greater than 4)= = 6 possible outcomes 3 Course 1

12 -4 Theoretical Probability Example 3 What is the probability of this fair spinner landing on 1 or 2? There are three possible outcomes when spinning this spinner: 1, 2, or 3. All are equally likely because the spinner is fair. P(3)= _________ 3 possible outcomes There are two ways for the spinner to land on 1 or 2. 2 ways event can occur __ 2 _________ = P(3)= 3 possible outcomes 3 Course 1

12 -4 Theoretical Probability Example 4 What is the probability of rolling a number less than 4 on a fair number cube? There are six possible outcomes when a fair number cube is rolled: 1, 2, 3, 4, 5, or 6. All are equally likely. There are 3 ways to roll a number greater than 4: 3, 2 or 1. P(less than 4)= _________ 6 possible outcomes 3 ways events can occur 1 __ __________ = P(less than 4)= 6 possible outcomes 2 Course 1

12 -4 Theoretical Probability When you combine all the ways that an event can NOT happen, you have the complement of the event. Course 1

12 -4 Theoretical Probability Example 5: Finding the Complement of an Event Suppose there is a 45% chance of snow tomorrow. What is the probability that it will not snow? In this situation there are two possible outcomes, either it will snow or it will not snow. P(snow) + P(not snow) = 100% 45% + P(not snow) = 100% -45% _____ P(not snow) = 55% Course 1 Subtract 45% from each side.

12 -4 Theoretical Probability Example 6 Suppose there is a 35% chance of rain tomorrow. What is the probability that it will not rain? In this situation there are two possible outcomes, either it will rain or it will not rain. P(rain) + P(not rain) = 100% 35% + P(not rain) = 100% -35% _____ P(not rain) = 65% Course 1 Subtract 35% from each side.

12 -4 Theoretical Insert Lesson Probability Title Here Lesson Quiz Use the spinner shown for problems 1 -3. 1. 2. 3. 4. 2 __ P(2) 7 4 __ P(odd number) 7 4 __ P(factor of 6) 7 Suppose there is a 2% chance of spinning the winning number at a carnival game. What is the probability of not winning? 98% Course 1

12 -2 Experimental Probability An experiment is an activity involving chance that can have different results. Flipping a coin and rolling a number cube are examples of experiments. The different results that can occur are called outcomes of the experiment. If you are flipping a coin, heads is one possible outcome. Course 1

12 -2 Experimental Probability Performing an experiment is one way to estimate the probability of an event. If an experiment is repeated many times, the experimental probability of an event is the ratio of the number of times the event occurs to the total number of times the experiment is performed. Course 1

12 -2 Experimental Probability Writing Math The probability of an event can be written as P(event). P(blue) means “the probability that blue will be the outcome. ” Course 1

12 -2 Experimental Probability Example 1: Comparing Experimental Probabilities Erika tossed a cylinder 30 times and recorded whether it landed on one of its bases or on its side. Based on Erika’s experiment, which way is the cylinder more likely to land? Outcome Frequency On a base On its side llll llll l Find the experimental probability of each outcome. Course 1