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Transparency 6. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 6-5b. Objective. Find and compare experimental and theoretical probabilities. Example 6-5b. Vocabulary. Experimental probability.

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  1. Transparency 6 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

  3. Example 6-5b Objective Find and compare experimental and theoretical probabilities

  4. Example 6-5b Vocabulary Experimental probability An estimated probability based on the relative frequency of positive outcomes occurring during an experiment

  5. Example 6-5b Vocabulary Theoretical probability The ratio of the number of ways an event can occur to the number of possible outcomes

  6. Example 6-5b Vocabulary Sample space A set of all possible outcomes

  7. Lesson 6 Contents Example 1Experimental Probability Example 2Experimental and Theoretical Probability Example 3Experimental and Theoretical Probability Example 4Predict Future Events Example 5Predict Future Events

  8. Example 6-1a A spinner is spun 50 times, and it lands on the color blue 15 times. What is the experimental probability of spinning blue? probability of spinning blue Write probability statement P(blue) = Write probability formula Replace numerator with 15 Replace denominator with 50 1/5

  9. Example 6-1a A spinner is spun 50 times, and it lands on the color blue 15 times. What is the experimental probability of spinning blue?  5 P(blue) = Find the GCF = 5  5 Divide GCF into numerator and denominator Answer: P(blue) = 1/5

  10. Example 6-1b A marble is pulled from a bag of colored marbles 30 times and 18 of the pulls results in a yellow marble. What is the experimental probability of pulling a yellow marble? Answer: P(yellow) = 1/5

  11. Example 6-2a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Find the experimental probability of rolling a 5. Find the experimental probability of rolling a 5 Write probability statement Write probability formula 2/5

  12. Example 6-2a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Find the experimental probability of rolling a 5. Find the experimental probability of rolling a 5 4 P(5) = 30 Replace numerator with 4 Replace denominator with 30 2/5

  13. Example 6-2a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Find the experimental probability of rolling a 5. Find the experimental probability of rolling a 5 4  2 P(5) = Find the GCF = 2  2 30 Answer: Divide GCF into numerator and denominator 2 P(5) = 15 2/5

  14. Example 6-2b The graph shows the result of an experiment in which a coin was tossed 150 times. Find the experimental probability of tossing heads for this experiment. Answer: P(heads) = 2/5

  15. Example 6-3a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Compare the experimental probability of rolling a 5 to its theoretical probability. probability of rolling a 5 Determine theoretical probability Write probability statement Write probability formula 3/5

  16. Example 6-3a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Compare the experimental probability of rolling a 5 to its theoretical probability. probability of rolling a 5 Determine theoretical probability Replace numerator with 1 1 P(5) = 6 Replace denominator with 6 since there are 6 numbers 3/5

  17. Example 6-3a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Compare the experimental probability of rolling a 5 to its theoretical probability. probability of rolling a 5 Determine theoretical probability 1 P(5) = 6 Determine experimental probability 2 You figured experimental probability for this data in Example 2, use it P(5) = 15 3/5

  18. Example 6-3a The graph below shows the results of an experiment in which a number cube is rolled 30 times. Compare the experimental probability of rolling a 5 to its theoretical probability. Experimental probability Theoretical probability 1 2 P(5) = P(5) = 6 15 P(5) = 0.17 Exp P(5) = 0.13 The P(5) = 0.17 Convert each fraction to a decimal Answer: Theoretical probability is greater than experimental probability Compare decimals by lining up decimals places 3/5

  19. Example 6-3b The graph shows the result of an experiment in which a coin was tossed 150 times. Compare the experimental probability of tossing heads to its theoretical probability. = 0.50 Theoretical Experimental = 0.53 Answer: Theoretical probability is greater than experimental probability 3/5

  20. Example 6-4a MOVIES In a survey, 50 people were asked to pick which movie they would see this weekend. Twenty chose Horror Story, 15 chose The Ink Well, 10 chose The Monkey House, and 5 chose Little Rabbit. What is the experimental probability of someone wanting to see The Monkey House? experimental probability see The Monkey House number of time The Monkey House chosen P(The Monkey House) = number of possible times chosen Write probability statement Write probability formula 4/5

  21. Example 6-4a MOVIES In a survey, 50 people were asked to pick which movie they would see this weekend. Twenty chose Horror Story, 15 chose The Ink Well, 10 chose The Monkey House, and 5 chose Little Rabbit. What is the experimental probability of someone wanting to see The Monkey House? experimental probability see The Monkey House number of time The Monkey House chosen P(The Monkey House) = number of possible times chosen 10 P(The Monkey House) = 50 Replace numerator with 10 Replace denominator with 50 4/5

  22. Example 6-4a MOVIES In a survey, 50 people were asked to pick which movie they would see this weekend. Twenty chose Horror Story, 15 chose The Ink Well, 10 chose The Monkey House, and 5 chose Little Rabbit. What is the experimental probability of someone wanting to see The Monkey House? experimental probability see The Monkey House number of time The Monkey House chosen P(The Monkey House) = number of possible times chosen 10  10 P(The Monkey House) = 50 Find the GCF = 10  10 Answer: Divide GCF into numerator and denominator 1 P(The Monkey House) = 5 4/5

  23. Example 6-4b SPORTSIn a survey, 100 people were asked to pick which sport they would watch on TV over the weekend. Thirty-five chose football, 20 chose basketball, 25 chose hockey, and 20 chose soccer. What is the experimental probability of someone wanting to watch football? Answer: P(football) = 4/5

  24. Example 6-5a In a survey, 50 people were asked to pick which movie they would see this weekend. Twenty chose Horror Story, 15 chose The Ink Well, 10 chose The Monkey House, and 5 chose Little Rabbit. Suppose 300 people are expected to attend a movie theater this weekend to see one of the four movies. How many can be expected to see The Monkey House? Suppose 300 people are expected to attend Use the probability for The Monkey House from example 4 Write a proportion 300 are expected to attend (total) Define variable 5/5

  25. Example 6-5a Find the cross products. Multiply Ask “what is being done to the variable?” 5x = 1(300) 5x = 1(300) 5x = 300 The variable is being multiplied by 5 5x = 300 5 5 Do the inverse on both sides of the equal sign Bring down 5x = 300 Using the fraction bar, divide both sides by 5 5/5

  26. Example 6-5a Combine “like” terms Use the Identity Property of Multiplication to multiply 1  x 5x = 1(300) 5x = 1(300) Add dimensional analysis 5x = 300 How many can be expected to see The Monkey House? 5x = 300 5 5 1  x = 60 Answer: x = 60 people see Monkey House 5/5

  27. Example 6-5b * In a survey, 100 people were asked to pick which sport they would watch on TV over the weekend. Thirty-five chose football, 20 chose basketball, 25 chose hockey, and 20 chose soccer. Suppose 1,500 people are expected to watch sports on TV this weekend. How many can be expected to watch football? Answer: x = 525 people watch football 5/5

  28. End of Lesson 6 Assignment

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