Experimental Probability 10-5 Experimental Probability Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

Warm Up: Part I Write the equivalent percent. 1. 2. 3. 4. Write the equivalent fraction. 30% 25% 20% 16% 5. 50% 6. 10% 7. 40% 8. 35%

Warm Up: Part II Write the equivalent decimal. 9. 18% 10. 50% 11. 12. 0.18 0.5 0.2 0.9

Objectives Determine the experimental probability of an event. Use experimental probability to make predictions.

Vocabulary experiment experimental probability trial prediction outcome sample space event probability

An experiment is an activity involving chance An experiment is an activity involving chance. Each repetition or observation of an experiment is a trial, and each possible result is an outcome. The sample space of an experiment is the set of all possible outcomes.

Example 1: Identifying Sample Spaces and Outcomes Identify the sample space and the outcome shown for each experiment. A. Rolling a number cube Sample space:{1, 2, 3, 4, 5, 6} Outcome shown: 4 B. Spinning a spinner Sample space:{red, green, orange, purple} Outcome shown: green

Check It Out! Example 1 Identify the sample space and the outcome shown for the experiment: rolling a number cube. Sample space: {1, 2, 3, 4, 5, 6} Outcome shown: 3

An event is an outcome or set of outcomes in an experiment An event is an outcome or set of outcomes in an experiment. Probability is the measure of how likely an event is to occur. Probabilities are written as fractions or decimals from 0 to 1, or as percents from 0% to 100%.

As likely as not Impossible Certain Unlikely Likely 0% 50% 100% Events with a probability of 0% never happen. 50% Events with a probability of 50% have the same chance of happening as not. 100% Events with a probability of 100% always happen.

Example 2: Estimating the Likelihood of an Event Write impossible, unlikely, as likely as not, likely, or certain to describe each event. A. A shoe selected from a pair of shoes fits the right foot. as likely as not B. Katrina correctly guesses the last digit of a phone number. unlikely C. Max pulls a green marble from a bag of all green marbles. certain D. A randomly selected month contains the letter R. likely

Check It Out! Example 2 Write impossible, unlikely, as likely as not, likely, or certain to describe the event: Anthony rolls a number less than 7 on a standard number cube. The highest number on a standard number cube is 6. Thus it is certain the number will be less than 7.

You can estimate the probability of an event by performing an experiment. The experimental probability of an event is the ratio of the number of times the event occurs to the number of trials. The more trials performed, the more accurate the estimate will be.

Example 3A: Finding Experimental Probability An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability of the event. Outcome Frequency Green 15 Orange 10 Purple 8 Pink 7 Spinner lands on orange

Example 3B: Finding Experimental Probability An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability of the event. Outcome Frequency Green 15 Orange 10 Purple 8 Pink 7 Spinner does not land on green

Check It Out! Example 3a An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability of each event. Outcome Frequency Red 7 Blue 8 Green 5 Spinner lands on red

Check It Out! Example 3b An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability of each event. Outcome Frequency Red 7 Blue 8 Green 5 Spinner does not land on red

You can use experimental probability to make predictions You can use experimental probability to make predictions. A prediction is an estimate or guess about something that has not yet happened.

Example 4A: Quality Control Application A manufacturer inspects 500 strollers and finds that 498 have no defects. What is the experimental probability that a stroller chosen at random has no defects? Find the experimental probability that a stroller has no defects. = 99.6% The experimental probability that a stroller has no defects is 99.6%.

Example 4B: Manufacturing Application A manufacturer inspects 500 strollers and finds that 498 have no defects. The manufacturer shipped 3500 strollers to a distribution center. Predict the number of strollers that are likely to have no defects. Find 99.6% of 3500. 0.996(3500) = 3486 The prediction is that 3486 strollers will have no defects.

Check It Out! Example 4a A manufacturer inspects 1500 electric toothbrush motors and finds 1497 have no defects. What is the experimental probability that a motor chosen at random will have no defects? Find the experimental probability that a motor has no defects. = 99.8%

Check It Out! Example 4b A manufacturer inspects 1500 electric toothbrush motors and finds 1497 have no defects. There are 35,000 motors in a warehouse. Predict the number of motors that are likely to have no defects. Find 99.8% of 35,000. 0.998(35000) = 34930 The prediction is that 34,930 motors will have no defects.

Lesson Quiz: Part I 1. Identify the sample space and the outcome shown for selecting a marble. Sample space: {red, green, yellow} Outcome shown: red

Lesson Quiz: Part II 2. An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability of landing on blue. Outcome Frequency Red 9 Blue 6 Yellow 5

Lesson Quiz: Part III 3. The neighbors’ dog barked at Tana the last 4 out of 5 times she walked by their house. a. What is the experimental probability that the dog barks at Tana when she walks past the house? 80% b. Predict the number of times the dog will bark at Tana if she walks past the house 45 times. 36