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# Int Math 2 Section 4-1 1011

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Experiments and Probabilities

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• ### Int Math 2 Section 4-1 1011

1. 1. Chapter 4 Probability
2. 2. SECTION 4-1Experiments and Probabilities
3. 3. Essential QuestionsHow do you collect data with experiments?How do you use data to ﬁnd experimentalprobabilities?Where you’ll see this: Music, market research, games, statistics, probability
4. 4. Vocabulary1. Experiment:2. Relative Frequency:3. Experimental Probability:
5. 5. Vocabulary1. Experiment: An activity used to produce data that is observed and recorded2. Relative Frequency:3. Experimental Probability:
6. 6. Vocabulary1. Experiment: An activity used to produce data that is observed and recorded2. Relative Frequency: Comparing the number of times an outcome occurs to the total number of observations3. Experimental Probability:
7. 7. Vocabulary1. Experiment: An activity used to produce data that is observed and recorded2. Relative Frequency: Comparing the number of times an outcome occurs to the total number of observations3. Experimental Probability: The likelihood an event (E) is going to occur
8. 8. Vocabulary1. Experiment: An activity used to produce data that is observed and recorded2. Relative Frequency: Comparing the number of times an outcome occurs to the total number of observations3. Experimental Probability: The likelihood an event (E) is going to occur Number of favorable outcomes P( E ) = Total number of possible outcomes
9. 9. ActivityObtain a coin and ﬂip it 30 times. Keep track of your results in the table.
10. 10. ActivityObtain a coin and ﬂip it 30 times. Keep track of your results in the table. Number of Tails Number of Heads
11. 11. Activity Obtain a coin and ﬂip it 30 times. Keep track of your results in the table. Number of Tails Number of Heads What is the ratio of heads up to the total number oftosses that you had? This is P(Heads), or the probability of ﬂipping a coin and landing on heads.
12. 12. Experimental Probability
13. 13. Experimental Probability Number of favorable outcomes P( E ) = Total number of possible outcomes
14. 14. Example 1Maggie Brann gave samples of a new lipstick and asked the women who received the samples to rate the lipstickaccording to certain standards of appeal. The results of the survey are below: Scores 50-59 60-69 70-79 80-89 90-99Frequency 1 4 2 6 2 What is the experimental probability that a woman who received a lipstick gave it a rating of at least 80?
15. 15. Example 1Maggie Brann gave samples of a new lipstick and asked the women who received the samples to rate the lipstickaccording to certain standards of appeal. The results of the survey are below: Scores 50-59 60-69 70-79 80-89 90-99Frequency 1 4 2 6 2 What is the experimental probability that a woman who received a lipstick gave it a rating of at least 80? P(Score ≥ 80)
16. 16. Example 1Maggie Brann gave samples of a new lipstick and asked the women who received the samples to rate the lipstickaccording to certain standards of appeal. The results of the survey are below: Scores 50-59 60-69 70-79 80-89 90-99Frequency 1 4 2 6 2 What is the experimental probability that a woman who received a lipstick gave it a rating of at least 80? 6+2 P(Score ≥ 80) = 15
17. 17. Example 1Maggie Brann gave samples of a new lipstick and asked the women who received the samples to rate the lipstickaccording to certain standards of appeal. The results of the survey are below: Scores 50-59 60-69 70-79 80-89 90-99Frequency 1 4 2 6 2 What is the experimental probability that a woman who received a lipstick gave it a rating of at least 80? 6+2 8 P(Score ≥ 80) = = 15 15
18. 18. Example 1Maggie Brann gave samples of a new lipstick and asked the women who received the samples to rate the lipstickaccording to certain standards of appeal. The results of the survey are below: Scores 50-59 60-69 70-79 80-89 90-99Frequency 1 4 2 6 2 What is the experimental probability that a woman who received a lipstick gave it a rating of at least 80? 6+2 8 P(Score ≥ 80) = = = 53 1 3 % 15 15
19. 19. Example 2 What is the probability that a dart thrown at this dartboard will land in the bull’s-eye? The radius of thesmallest circle is 2 cm, and each band is also 2 cm wide.
20. 20. Example 2 What is the probability that a dart thrown at this dartboard will land in the bull’s-eye? The radius of thesmallest circle is 2 cm, and each band is also 2 cm wide. P(Bulls-eye)
21. 21. Example 2 What is the probability that a dart thrown at this dartboard will land in the bull’s-eye? The radius of thesmallest circle is 2 cm, and each band is also 2 cm wide. P(Bulls-eye) Area of smallest circle = Area of largest circle
22. 22. Example 2 What is the probability that a dart thrown at this dartboard will land in the bull’s-eye? The radius of thesmallest circle is 2 cm, and each band is also 2 cm wide. P(Bulls-eye) Area of smallest circle = Area of largest circle 2 π (2) = 2 π (6)
23. 23. Example 2 What is the probability that a dart thrown at this dartboard will land in the bull’s-eye? The radius of thesmallest circle is 2 cm, and each band is also 2 cm wide. P(Bulls-eye) Area of smallest circle = Area of largest circle π (2) = 4 2 = π (6) 2 36
24. 24. Example 2 What is the probability that a dart thrown at this dartboard will land in the bull’s-eye? The radius of thesmallest circle is 2 cm, and each band is also 2 cm wide. P(Bulls-eye) Area of smallest circle = Area of largest circle π (2) = 4 = 1 2 = π (6) 2 36 9
25. 25. Example 2 What is the probability that a dart thrown at this dartboard will land in the bull’s-eye? The radius of thesmallest circle is 2 cm, and each band is also 2 cm wide. P(Bulls-eye) Area of smallest circle = Area of largest circle π (2) = 4 = 1 2 = π (6) 2 36 9 = 11 1 9 %
26. 26. Example 2 What is the probability that a dart thrown at this dartboard will land in the bull’s-eye? The radius of thesmallest circle is 2 cm, and each band is also 2 cm wide. P(Bulls-eye) Area of smallest circle = Area of largest circle π (2) = 4 = 1 2 = π (6) 2 36 9 = 11 1 9 % Favorable area P(Area) = Total area
27. 27. Problem Set
28. 28. Problem Set p. 152 #1-20“Liberty means responsibility. That is why most men dread it.” - George Bernard Shaw