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4. Example 6-6b Objective Find experimental probability

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

6. Example 6-6b Vocabulary Theoretical probability Probability based on known characteristics or facts

7. Example 6-6b Vocabulary Proportion A statement of equality of two or more ratios

8. Lesson 6 Contents Example 1Experimental Probability Example 2Experimental Probability Example 3Theoretical Probability Example 4Experimental Probability Example 5Use Probability to Predict Example 6Use Probability to Predict

9. Example 6-1a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. According to the experimental probability, is Nikki more likely to get all heads or no heads on the next toss? 12no heads 30one head 32two heads 6all heads Number of Tosses Result 1/6 Since it asks for experimental probability use the data in the chart

10. Example 6-1a 12no heads 30one head 32two heads 6all heads Number of Tosses Result 1/6 Write the probability statement for all heads Is Nikki more likely to get all heads or no heads on the next toss? P(all heads) = Number of all heads Write formula for probability Total number of tosses Replace numerator with number of all heads P(all heads) = 6 Add total number of tosses 80

11. Example 6-1a 12no heads 30one head 32two heads 6all heads Number of Tosses Result 1/6 Simplify fraction using the calculator Is Nikki more likely to get all heads or no heads on the next toss? P(all heads) = Number of all heads Total number of tosses P(all heads) = 6 80 P(all heads) = 3 40

12. Example 6-1a 12no heads 30one head 32two heads 6all heads Number of Tosses Result 1/6 Write the probability statement for no heads Is Nikki more likely to get all heads or no heads on the next toss? P(no heads) = Number of no heads Write formula for probability Total number of tosses Replace numerator with number of no heads P(all heads) = 3 Add total number of tosses 40 P(no heads) = 12 80

13. Example 6-1a 12no heads 30one head 32two heads 6all heads Number of Tosses Result 1/6 Is Nikki more likely to get all heads or no heads on the next toss? P(no heads) = Number of no heads Total number of tosses P(all heads) = 3 40 P(no heads) = 12 80 Simplify fraction using the calculator P(no heads) = 3 20

14. Example 6-1a 12no heads 30one head 32two heads 6all heads Number of Tosses Result 1/6 Is Nikki more likely to get all heads or no heads on the next toss? P(no heads) = P(all heads) = 3 40 To compare probabilities, must convert to a decimal 3 20 0.075 Make sure to line up the decimals for comparison 0.15 Compare decimals No heads has a greater probability Answer: No heads

15. Example 6-1b Marcus is conducting an experiment to find the probability of getting various results when four coins are tossed. The results of his experiment are given below. According to the experimental probability, is Marcus more likely to get all heads or no heads on the next toss? Answer: all heads 7one head 20two heads 12three heads 6all heads Number of Tosses Result 5no heads 1/6

16. Example 6-2a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. How many possible outcomes are there for tossing three coins if order is important? 12no heads 30one head 32two heads 6all heads Number of Tosses Result Remember: To do this must multiply the number of outcomes of each event by the other outcomes 2/6 To find the number of outcomes, use the Fundamental Counting Principle

17. Example 6-2a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. How many possible outcomes are there for tossing three coins if order is important? 12no heads 30one head 32two heads 6all heads Number of Tosses Result 2/6 Each coin that is flipped has 2 possible outcomes 1 st Coin 2 2 nd Coin  2 3 rd Coin  2

18. Example 6-2a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. How many possible outcomes are there for tossing three coins if order is important? 12no heads 30one head 32two heads 6all heads Number of Tosses Result 2/6 Multiply 1 st Coin 2 2 nd Coin  2 3 rd Coin  2 8 Answer: Add dimensional analysis possible outcomes

19. Example 6-2b Marcus is conducting an experiment to find the probability of getting various results when four coins are tossed. The results of his experiment are given below. How many possible outcomes are there for tossing four coins if order is important? Answer: 16 possible outcomes 7one head 20two heads 12three heads 6all heads Number of Tosses Result 5no heads 2/6

20. Example 6-3a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads? 12no heads 30one head 32two heads 6all heads Number of Tosses Result 3/6 Remember: theoretical probability is what “might” happen The experimental (actual) data has nothing to do with theoretical

21. Example 6-3a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads? 3/6 Write the probability statement for heads P( heads) = Number of heads Total number of outcomes Write formula for heads

22. Example 6-3a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads? 3/6 Replace numerator with number of heads on a coin P( heads) = Number of heads Total number of outcomes P( heads) = 1 Replace denominator with number of sides a coin has 2

23. Example 6-3a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads? 3/6 The probability of each coin being heads will be the same P( heads) = Number of heads Total number of outcomes P( heads) = 1 2 Write probability statement for “all heads” P(all heads) =

24. Example 6-3a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads? 3/6 Multiply the probability of each coin P( heads) = Number of heads Total number of outcomes P( heads) = 1 2 P(all heads) = 1 1 1 2 22   1 8

25. Example 6-3a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads? 3/6 Write the probability statement for no heads P( no heads) = Number of no heads Total number of outcomes Write formula for no heads

26. Example 6-3a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads? 3/6 Replace numerator with number of no heads on a coin P(no heads) = Number of no heads Total number of outcomes P(no heads) = 1 Replace denominator with number of sides a coin has 2

27. Example 6-3a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads? 3/6 The probability of each coin being no heads will be the same P( no heads) = Number of heads Total number of outcomes P(no heads) = 1 2 Write probability statement for “all heads” P(all no heads) =

28. Example 6-3a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads? 3/6 Multiply the probability of each coin P( heads) = Number of heads Total number of outcomes P( heads) = 1 2 P(all no heads) = 1 1 1 2 22   1 8

29. Example 6-3a Nikki is conducting an experiment to find the probability of getting various results when three coins are tossed. The results of her experiment are given below. What is the theoretical probability for all heads and for no heads. Is the theoretical probability greater for tossing all heads or no heads? 3/6 Since both probabilities are the same P( all no heads) = 1 8 P( all heads) = 1 8 Is no heads? the theoretical probability greater for tossing all heads or The probabilities have equal chances Answer:

30. Example 6-3b Marcus is conducting an experiment to find the probability of getting various results when four coins are tossed. The results of his experiment are given below. Is the theoretical probability greater for tossing all heads or no heads? What is the theoretical probability of each? 7one head 20two heads 12three heads 6all heads Number of Tosses Result 5no heads P(all heads) = P(all no heads) = Answer: 3/6 The probabilities have equal chances

31. Example 6-4a MARKETING Eight hundred adults were asked whether they were planning to stay home for winter vacation. Of those surveyed, 560 said that they were. What is the experimental probability that an adult planned to stay home for winter vacation? P(stay home) = 4/6 Write the probability statement staying home What is the experimental probability that an adult planned to stay home Write the formula for probability Number stay home Total Adults

32. Example 6-4a MARKETING Eight hundred adults were asked whether they were planning to stay home for winter vacation. Of those surveyed, 560 said that they were. What is the experimental probability that an adult planned to stay home for winter vacation? P(stay home) = 4/6 Replace numerator with number planning to stay home What is the experimental probability that an adult planned to stay home Number stay home Total Adults P(stay home) = 560 Replace denominator with total asked 800

33. Example 6-4a MARKETING Eight hundred adults were asked whether they were planning to stay home for winter vacation. Of those surveyed, 560 said that they were. What is the experimental probability that an adult planned to stay home for winter vacation? P(stay home) = 4/6 Simplify with calculator What is the experimental probability that an adult planned to stay home Number stay home Total Adults P(stay home) = 560 800 P(stay home) = Answer:

34. Example 6-4b MARKETING Five hundred adults were asked whether they were planning to stay home for New Year’s Eve. Of those surveyed, 300 said that they were. What is the experimental probability that an adult planned to stay home for New Year’s Eve? Answer: P(stay home) = 4/6

35. Example 6-5a Answer: Experimental probability, wins have already happened MATH TEAM Over the past three years, the probability that the school math team would win a meet is Is this probability experimental or theoretical? Explain. Experimental: What has happened Theoretical: What will happen 5/6 “over the past 3 years” refers to what has happened

36. Example 6-5b Answer: Experimental; it is based on actual results. SPEECH AND DEBATE Over the past three years, the probability that the school speech and debate team would win a meet is Is this probability experimental or theoretical? Explain. 5/6

37. Example 6-6a MATH TEAM Over the past three years, the probability that the school math team would win a meet is If the team wants to win 12 more meets in the next 3 years, how many meets should the team enter? Use a proportion to solve this problem 6/6 Write the probability as the first ratio Remember: a ratio is a part over the whole

38. Example 6-6a MATH TEAM Over the past three years, the probability that the school math team would win a meet is If the team wants to win 12 more meets in the next 3 years, how many meets should the team enter? 6/6 “wants to win” refers to a part of the total wins Define the variable Cross multiply to find the value of “x”

39. Example 6-6a 3x Cross multiply 6/6 = 5(12) Multiply Ask “what is being done to the variable?” The variable is being multiplied by 3 Do the inverse on both sides of the equal sign

40. Example 6-6a Answer: 3x Bring down 3x = 60 6/6 = 5(12) Using a fraction bar, divide both sides by 3 Combine “like” terms 1  x = 20 Use the Identity Property to multiply 1  x x = 20 Add dimensional analysis How many meets should the team enter? meets

41. Example 6-6b SPEECH AND DEBATE Over the past three years, the probability that the school speech and debate team would win a meet is If the team wants to win 20 more meets in the next 3 years, how many meets should the team enter? Answer: x = 25 meets * 6/6

42. End of Lesson 6 Assignment Lesson 8:6Experimental Probability3 - 17 All