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Transparency 6. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 6-6b. Objective. Find experimental probability. Example 6-6b. 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 6-6b Objective Find experimental probability

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

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

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

  7. 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

  8. Result Number of Tosses all heads 6 two heads 32 one head 30 no heads 12 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? Since it asks for experimental probability use the data in the chart 1/6

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

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

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

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

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

  14. Result Number of Tosses all heads 6 three heads 12 two heads 20 one head 7 no heads 5 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 1/6

  15. Result Number of Tosses all heads 6 two heads 32 one head 30 no heads 12 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? To find the number of outcomes, use the Fundamental Counting Principle Remember: To do this must multiply the number of outcomes of each event by the other outcomes 2/6

  16. Result Number of Tosses all heads 6 two heads 32 one head 30 no heads 12 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? 1st Coin 2nd Coin 3rd Coin 2  2  2 Each coin that is flipped has 2 possible outcomes 2/6

  17. Result Number of Tosses all heads 6 two heads 32 one head 30 no heads 12 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? 1st Coin 2nd Coin 3rd Coin 2  2  2 Answer: possible outcomes 8 Multiply Add dimensional analysis 2/6

  18. Result Number of Tosses all heads 6 three heads 12 two heads 20 one head 7 no heads 5 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 2/6

  19. Result Number of Tosses all heads 6 two heads 32 one head 30 no heads 12 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? Remember: theoretical probability is what “might” happen The experimental (actual) data has nothing to do with theoretical 3/6

  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? Number of heads P( heads) = Total number of outcomes Write the probability statement for heads Write formula for heads 3/6

  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? Number of heads P( heads) = Total number of outcomes 1 P( heads) = Replace numerator with number of heads on a coin 2 Replace denominator with number of sides a coin has 3/6

  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? Number of heads P( heads) = Total number of outcomes 1 P( heads) = The probability of each coin being heads will be the same 2 P(all heads) = Write probability statement for “all heads” 3/6

  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? Number of heads P( heads) = Total number of outcomes 1 P( heads) = Multiply the probability of each coin 2 1 1 1  P(all heads) =  2 2 2 1 P(all heads) = 8 3/6

  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? Number of no heads P( no heads) = Total number of outcomes Write the probability statement for no heads Write formula for no heads 3/6

  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? Number of no heads P(no heads) = Total number of outcomes 1 P(no heads) = Replace numerator with number of no heads on a coin 2 Replace denominator with number of sides a coin has 3/6

  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? Number of heads P( no heads) = Total number of outcomes 1 P(no heads) = The probability of each coin being no heads will be the same 2 P(all no heads) = Write probability statement for “all heads” 3/6

  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? Number of heads P( heads) = Total number of outcomes 1 P( heads) = Multiply the probability of each coin 2 1 1 1  P(all no heads) =  2 2 2 1 P(all no heads) = 8 3/6

  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? Is the theoretical probability greater for tossing all heads or no heads? Since both probabilities are the same Answer: 1 P( all heads) = 8 1 P( all no heads) = 8 The probabilities have equal chances 3/6

  29. Result Number of Tosses all heads 6 three heads 12 two heads 20 one head 7 no heads 5 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? Answer: P(all heads) = P(all no heads) = The probabilities have equal chances 3/6

  30. Example 6-4a MARKETINGEight 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? What is the experimental probability that an adult planned to stay home Number stay home P(stay home) = Total Adults Write the probability statement staying home Write the formula for probability 4/6

  31. Example 6-4a MARKETINGEight 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? What is the experimental probability that an adult planned to stay home Number stay home P(stay home) = Total Adults Replace numerator with number planning to stay home 560 P(stay home) = 800 Replace denominator with total asked 4/6

  32. Example 6-4a MARKETINGEight 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? What is the experimental probability that an adult planned to stay home Number stay home P(stay home) = Total Adults Simplify with calculator 560 P(stay home) = 800 Answer: P(stay home) = 4/6

  33. Example 6-4b MARKETINGFive 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

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

  35. SPEECH AND DEBATEOver 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. Example 6-5b Answer: Experimental; it is based on actual results. 5/6

  36. MATH TEAMOver 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? Example 6-6a Use a proportion to solve this problem Write the probability as the first ratio Remember: a ratio is a part over the whole 6/6

  37. MATH TEAMOver 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? Example 6-6a “wants to win” refers to a part of the total wins Define the variable Cross multiply to find the value of “x” 6/6

  38. Example 6-6a Cross multiply Multiply 3x = 5(12) 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 6/6

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

  40. SPEECH AND DEBATEOver 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? Example 6-6b * Answer: x = 25 meets 6/6

  41. End of Lesson 6 Assignment

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