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# Integrated Math 2 Section 4-1

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Experiments and Probabilities

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### Integrated Math 2 Section 4-1

1. 1. Chapter 4 Probability
2. 2. SECTION 4-1 Experiments and Probabilities
3. 3. Essential Questions How do you collect data with experiments? How do you use data to ﬁnd experimental probabilities? Where you’ll see this: Music, market research, games, statistics, probability
4. 4. Vocabulary 1. Experiment: 2. Relative Frequency: 3. Experimental Probability:
5. 5. Vocabulary 1. Experiment: An activity used to produce data that is observed and recorded 2. Relative Frequency: 3. Experimental Probability:
6. 6. Vocabulary 1. Experiment: An activity used to produce data that is observed and recorded 2. Relative Frequency: Comparing the number of times an outcome occurs to the total number of observations 3. Experimental Probability:
7. 7. Vocabulary 1. Experiment: An activity used to produce data that is observed and recorded 2. Relative Frequency: Comparing the number of times an outcome occurs to the total number of observations 3. Experimental Probability: The likelihood an event (E) is going to occur
8. 8. Vocabulary 1. Experiment: An activity used to produce data that is observed and recorded 2. Relative Frequency: Comparing the number of times an outcome occurs to the total number of observations 3. Experimental Probability: The likelihood an event (E) is going to occur Number of favorable outcomes P( E ) = Total number of possible outcomes
9. 9. Activity Complete the activity from page 150: Flipping a coin
10. 10. Activity Complete the activity from page 150: Flipping a coin Number of Tails Number of Heads
11. 11. Activity Complete the activity from page 150: Flipping a coin Number of Tails Number of Heads P(Tails) = ?
12. 12. Example 1 Maggie Brann gave samples of a new lipstick and asked the women who received the samples to rate the lipstick according to certain standards of appeal. The results of the survey are below: Scores 50-59 60-69 70-79 80-89 90-99 Frequency 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?
13. 13. Example 1 Maggie Brann gave samples of a new lipstick and asked the women who received the samples to rate the lipstick according to certain standards of appeal. The results of the survey are below: Scores 50-59 60-69 70-79 80-89 90-99 Frequency 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)
14. 14. Example 1 Maggie Brann gave samples of a new lipstick and asked the women who received the samples to rate the lipstick according to certain standards of appeal. The results of the survey are below: Scores 50-59 60-69 70-79 80-89 90-99 Frequency 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
15. 15. Example 1 Maggie Brann gave samples of a new lipstick and asked the women who received the samples to rate the lipstick according to certain standards of appeal. The results of the survey are below: Scores 50-59 60-69 70-79 80-89 90-99 Frequency 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
16. 16. Example 1 Maggie Brann gave samples of a new lipstick and asked the women who received the samples to rate the lipstick according to certain standards of appeal. The results of the survey are below: Scores 50-59 60-69 70-79 80-89 90-99 Frequency 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
17. 17. Example 2 What is the probability that a dart thrown at this dartboard will land in the bull’s-eye? The radius of the smallest circle is 2 cm, and each band is also 2 cm wide.
18. 18. Example 2 What is the probability that a dart thrown at this dartboard will land in the bull’s-eye? The radius of the smallest circle is 2 cm, and each band is also 2 cm wide. P(Bull's-eye)
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 the smallest circle is 2 cm, and each band is also 2 cm wide. P(Bull's-eye) Area of smallest circle = Area of largest circle
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 the smallest circle is 2 cm, and each band is also 2 cm wide. P(Bull's-eye) Area of smallest circle = Area of largest circle 2 π (2) = 2 π (6)
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 the smallest circle is 2 cm, and each band is also 2 cm wide. P(Bull's-eye) Area of smallest circle = Area of largest circle π (2) = 4 2 = π (6) 2 36
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 the smallest circle is 2 cm, and each band is also 2 cm wide. P(Bull's-eye) Area of smallest circle = Area of largest circle π (2) = 4 = 1 2 = π (6) 2 36 9
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 the smallest circle is 2 cm, and each band is also 2 cm wide. P(Bull's-eye) Area of smallest circle = Area of largest circle π (2) = 4 = 1 2 = π (6) 2 36 9 = 11 1 9 %
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 the smallest circle is 2 cm, and each band is also 2 cm wide. P(Bull's-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
25. 25. Homework
26. 26. Homework p. 152 #1-20 “Liberty means responsibility. That is why most men dread it.” - George Bernard Shaw