1. Experimental Probability Lesson 3.6 Core Focus on Ratios, Rates and Statistics

2. Determine whether each probability is impossible, unlikely, equally likely, likely or certain. 1.You roll a 6 on a number cube. 2.There is a 0.8 chance of rain today. 3.You close your eyes or blink your eyes at least once in the next five minutes. 4.There is a 0.4 chance that the temperature will be greater than 60 degrees today. Write this probability as a percent and a simplified fraction. Warm-Up unlikely likely certain

3. Experimental Probability Find and interpret the experimental probability of an event. Lesson 3.6

4. Vocabulary Outcome One possible result from an experiment or probability event. Sample Space The set of all possible outcomes for an event. Use { } to list a sample space. Trial A single act of performing an experiment. Experimental Probability The ratio of the number of times an event occurs to the total number of trials. Good to Know! The notation P( ) is used for probabilities. Example: The probability of rolling a 2 with a number cube is written as P(2) or P(two).

5. Abram had 2 red marbles and 1 white marble in a bag. He chose the white marble. Identify the outcome and show the sample space for this experiment. He chose a white marble.Outcome: white The possible marbles Abram could have chosen are red, red or white. Sample Space = {red, red, white} Example 1

6. Experimental Probability

7. Nik took a jelly bean out of a bag without looking. He recorded the color. He placed it back in the bag. He did this several times. The results are shown in the table. a.Find the total number of trials. Find the total of the frequencies.4 + 12 + 8 + 24 = 48 Nik completed 48 trials. Example 2

8. Nik took a jelly bean out of a bag without looking. He recorded the color. He placed it back in the bag. He did this several times. The results are shown in the table. b.Find the experimental probability his next jelly bean will be red. Example 2 Continued… This is read, “The probability of picking a red is one-twelfth.”

9. Nik took a jelly bean out of a bag without looking. He recorded the color. He placed it back in the bag. He did this several times. The results are shown in the table. c.Find the experimental probability his next jelly bean will be green. Example 2 Continued…

10. Step 1Copy the chart below on your paper. Roll a number cube ten times. Record the number of times each number appears by using a tally mark in the chart. Step 2The table below shows some common fractions used when measuring in inches. Copy the table and convert each measurement to a decimal. a.How many trials have you done? b.Find P(roll a 3). a.How many trials have you done? b.Find P(roll a 3). Step 3Roll the number cube ten more times. Record the number of times each number appears using the chart from Step 1. a.How many trials have you done? b.Find P(roll a 3).

11. Step 4Roll the number cube ten more times. Record the number of times each number appears using the chart from Step 1. Continue adding tally marks. Step 5Roll the number cube ten more times. Record the number of times each number appears using the chart from Step 1. Continue adding tally marks. a.How many trials have you done? b.Find P(roll a 3). Step 6Which probability do you think is the most accurate estimate for the probability of rolling a 3 on your next turn? Explain your reasoning. a.How many trials have you done? b.Find P(roll a 3).

12. Suppose you entered a contest where you will throw bean bags through a hole in a piece of plywood as part of a fundraiser. On the day of the contest, you will throw the bean bag 100 times. Explain how you could create an experiment to predict how many tosses you will make without actually throwing the bean bag 100 times. Identify your outcomes, sample space and number of trials. Communication Prompt

13. 1.Identify the sample space: Tom rolls a regular six-sided number cube. 2.Sherlock put his music player on random play. It chose the same song 3 out of the last 12 times it played a song. What is the experimental probability it will play the same song for its next selection? 3.Charlie made 4 out of 5 free throws at basketball practice today. What is the experimental probability he will make a free throw at the game tonight? Exit Problems {1, 2, 3, 4, 5, 6}